Problem: Let's find the values of variables q and s by solving the following system of equations: 1. (40 * s) - (91 * q) = 37 2. (30 * s) + (12 * q) = 121

Mixtral 8x22B:

 Reasoning:

First, let's solve equation 1 for s:

s = (37 + 91q) / 40

Now, let's substitute this expression for s into equation 2:

30 * ((37 + 91q) / 40) + 12q = 121

Simplify the equation:

(30 * 37 + 30 * 91q) / 40 + 12q = 121

Multiply both sides by 40 to eliminate the fraction:

30 * 37 + 30 * 91q + 480q = 4840

Simplify further:

1110 + 2730q + 480q = 4840

Combine like terms:

3210q = 3730

Divide both sides by 3210:

q = 3730 / 3210

Simplify the fraction:

q = 1.16199378882

Now, let's substitute this value of q back into the expression for s:

s = (37 + 91 * 1.16199378882) / 40

Simplify the expression:

s = (37 + 105.719378882) / 40

s = 142.719378882 / 40

Simplify the fraction:

s = 3.56798447205

Therefore, the values of q and s are approximately 1.162 and 3.568, respectively.

### Answer: q ≈ 1.162, s ≈ 3.568

Expected answer: {q: 373/321, s: 2291/642}

Correct? No

Problem: Solve the following system of equations for the values of b and m: 4 * b + 44 * m = 180 and 79 * m - 6 * b = 48.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's solve the first equation for b:

4b + 44m = 180
4b = 180 - 44m
b = (180 - 44m) / 4

Now, let's substitute this expression for b into the second equation:

79m - 6((180 - 44m) / 4) = 48

Now, let's solve for m:

79m - (6 * 180 / 4) + (6 * 44m / 4) = 48
79m - 270 + 66m = 48
145m = 318
m = 318 / 145
m = 2.19 (rounded to two decimal places)

Now, let's substitute the value of m back into the expression for b:

b = (180 - 44 * 2.19) / 4
b = (180 - 96.36) / 4
b = 83.64 / 4
b = 20.91 (rounded to two decimal places)

Therefore, the values of b and m are:

b = 20.91
m = 2.19

### Answer: b = 20.91, m = 2.19

Expected answer: {b: 3027/145, m: 318/145}

Correct? No

Problem: Solve the following system of equations to find the values of o and g: 42 * o - 15 * g = 28 47 * o + 29 * g = 141.

Mixtral 8x22B:

 Reasoning:

Let's call the first equation (1) and the second equation (2).

We can solve this system of equations using the substitution or elimination method. I will use the elimination method.

First, we can multiply equation (1) by 29 and equation (2) by 15 to make the coefficients of g the same:

(1) * 29: 42o - 15g = 28 => 1218o - 435g = 812
(2) * 15: 47o + 29g = 141 => 705o + 435g = 2115

Now, we can add the two equations to eliminate g:

1218o - 435g + 705o + 435g = 812 + 2115
1923o = 2927

Now, we can solve for o:

o = 2927 / 1923

Now that we have the value of o, we can substitute it back into either equation (1) or (2) to find the value of g. Let's use equation (1):

42o - 15g = 28
42(2927/1923) - 15g = 28
1229.4 - 15g = 28

Now, we can solve for g:

15g = 1229.4 - 28
15g = 1201.4
g = 1201.4 / 15
g = 80.09333333333333

So, the values of o and g are:

o = 2927 / 1923 ≈ 1.521
g = 80.09333333333333

### Answer: o ≈ 1.521, g ≈ 80.093

Expected answer: {g: 4606/1923, o: 2927/1923}

Correct? No

Problem: Given the following system of equations, determine the values of v and o: The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's simplify the equations by dividing both sides of the first equation by 6 and both sides of the second equation by 15:

(2v - o) = 3.5
(15.2v - 9o) = 10

Now, let's multiply the first equation by 9 to eliminate o:

(18v - 9o) = 31.5

Now, let's subtract the second equation from the new equation:

(18v - 9o) - (15.2v - 9o) = 31.5 - 10

This simplifies to:

2.8v = 21.5

Now, let's solve for v:

v = 21.5 / 2.8 = <<21.5/2.8=7.678571428571429>>7.678571428571429

Now, let's substitute the value of v into the first equation to solve for o:

(2 * 7.678571428571429) - o = 3.5

This simplifies to:

15.357142857142858 - o = 3.5

Now, let's solve for o:

o = 15.357142857142858 - 3.5 = <<15.357142857142858-3.5=11.857142857142858>>11.857142857142858

Therefore, the values of v and o are approximately 7.68 and 11.86, respectively.

### Answer: v ≈ 7.68, o ≈ 11.86

Expected answer: {o: 83/7, v: 215/28}

Correct? No

Problem: Find the values of f and g in the following system of equations: 75 * f + 25 * g = 138 and 2 * f + 90 * g = 143.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. In this case, we will use the method of elimination.

First, we can multiply the second equation by 3 to make the coefficients of f in both equations equal:

3 * (2 * f + 90 * g) = 3 * 143
6 * f + 270 * g = 429

Now we have the following system of equations:

75 * f + 25 * g = 138
6 * f + 270 * g = 429

Next, we can subtract the first equation from the second equation to eliminate f:

(6 * f + 270 * g) - (75 * f + 25 * g) = 429 - 138
6 * f - 75 * f + 270 * g - 25 * g = 291
-69 * f + 245 * g = 291

Now we can solve for g:

245 * g = 291 + 69 * f
g = (291 + 69 * f) / 245

Next, we can substitute this expression for g back into the first equation to solve for f:

75 * f + 25 * ((291 + 69 * f) / 245) = 138
75 * f + (291 * 25 + 69 * 25 * f) / 245 = 138
75 * f + (7275 + 1725 * f) / 245 = 138
75 * f + 29.69387755102041 * f = 138 - 29.69387755102041
104.69387755102041 * f = 108.3061224489796
f = 108.3061224489796 / 104.69387755102041
f = 1.03448275862069

Now that we have the value of f, we can substitute it back into the expression for g to find its value:

g = (291 + 69 * 1.03448275862069) / 245
g = (291 + 71.33877551020408) / 245
g = 362.3387755102041 / 245
g = 1.47892887963307

Therefore, the values of f and g are approximately 1.034 and 1.479, respectively.

### Answer: f ≈ 1.034, g ≈ 1.479

Expected answer: {f: 1769/1340, g: 10449/6700}

Correct? No

Problem: Solve the following system of equations for variables y and n: the first equation is 194 = 4 * y + 14 * n and the second equation is 7 = 65 * n - 79 * y.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for y:

194 = 4y + 14n
194 - 14n = 4y
y = (194 - 14n)/4

Now, let's substitute this expression for y into the second equation:

7 = 65n - 79((194 - 14n)/4)
7 = 65n - 79(48.5 - 3.5n)
7 = 65n - 3816.5 + 276.5n
7 + 3816.5 = 65n + 276.5n
3823.5 = 341.5n
n = 3823.5/341.5
n = 11.2

Now that we have the value for n, we can substitute it back into the expression for y:

y = (194 - 14(11.2))/4
y = (194 - 156.8)/4
y = 37.2/4
y = 9.3

So the solution to the system of equations is y = 9.3 and n = 11.2.

### Answer: y = 9.3, n = 11.2

Expected answer: {n: 7677/683, y: 6256/683}

Correct? No

Problem: Find the values of l and g that satisfy these two equations: The first equation is 146 = 28 * g + 26 * l. The second equation is 6 = 41 * l - 53 * g.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using substitution or elimination method.

Using the elimination method, we can multiply the second equation by 28 and the first equation by 41 to eliminate g:

28 * (6) = 28 * (41 * l - 53 * g)
41 * (146) = 41 * (28 * g + 26 * l)

This simplifies to:

168 = 1148 * l - 1484 * g
6006 = 1148 * g + 1084 * l

Now, we can add the two equations to eliminate g:

168 + 6006 = 1148 * l - 1484 * g + 1148 * g + 1084 * l
6174 = 2232 * l

Now, we can solve for l:

l = 6174 / 2232
l = <<6174/2232=2.7666666666666665>>2.7666666666666665

Now, we can substitute the value of l back into one of the original equations to find g:

146 = 28 * g + 26 * (2.7666666666666665)
146 = 28 * g + 71.99999999999999

Now, we can solve for g:

g = (146 - 71.99999999999999) / 28
g = <<(146-71.99999999999999)/28=2.7666666666666665>>2.7666666666666665

So, the values of l and g that satisfy the given equations are:

l = 2.7666666666666665
g = 2.7666666666666665

### Answer: l = 2.7666666666666665, g = 2.7666666666666665

Expected answer: {g: 2915/1263, l: 3953/1263}

Correct? No

Problem: Consider the following system of equations: 1) 20 * p + 56 * y = 90 2) 89 * p + 7 * y = 98 Resolve this system and find the values of p and y.

Mixtral 8x22B:

 To solve this system of equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, let's multiply the first equation by 7 and the second equation by 56 to make the coefficients of y the same:

1) 7 * (20 * p + 56 * y) = 7 * 90
2) 56 * (89 * p + 7 * y) = 56 * 98

This gives us:

1) 140 * p + 392 * y = 630
2) 5024 * p + 392 * y = 5408

Now, let's subtract the first equation from the second equation to eliminate y:

(5024 * p + 392 * y) - (140 * p + 392 * y) = 5408 - 630

This simplifies to:

4884 * p = 4778

Now, let's solve for p:

p = 4778 / 4884

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 4778 and 4884 is 2.

p = (4778 / 2) / (4884 / 2)

p = 2389 / 2442

Now, let's substitute the value of p back into one of the original equations to solve for y. Let's use the first equation:

20 * p + 56 * y = 90

Substitute the value of p:

20 * (2389 / 2442) + 56 * y = 90

Now, let's solve for y:

56 * y = 90 - 20 * (2389 / 2442)

56 * y = 90 - (47780 / 2442)

56 * y = (216000 / 2442) - (47780 / 2442)

56 * y = (216000 - 47780) / 2442

56 * y = 168220 / 2442

Now, let's divide both sides by 56 to solve for y:

y = (168220 / 2442) / 56

y = 3004 / 436

Now, let's simplify this fraction by dividing both the numerator and the denominator by their GCD. The GCD of 3004 and 436 is 4.

y = (3004 / 4) / (436 / 4)

y = 751 / 109

Therefore, the solution to the system of equations is:

p = 2389 / 2442
y = 751 / 109

### Answer: p = 2389/2442, y = 751/109

Expected answer: {p: 347/346, y: 3025/2422}

Correct? No

Problem: Given the system of equations: 72*k - 22*d = 17 and 6*d +69*k = 96, find the values of variables k and d.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 3 to make the coefficients of d the same in both equations:

3*(72*k - 22*d) = 3*17
216*k - 66*d = 51

Now, we can add the two equations to eliminate d:

(216*k - 66*d) + (6*d + 69*k) = 51 + 96
285*k = 147

Now, we can solve for k:

k = 147/285
k = 1/2

Now that we have the value of k, we can substitute it back into one of the original equations to find the value of d. Let's use the second equation:

6*d + 69*(1/2) = 96
6*d + 34.5 = 96
6*d = 96 - 34.5
6*d = 61.5
d = 61.5/6
d = 10.25

Therefore, the values of the variables are k = 1/2 and d = 10.25.

### Answer: k = 1/2, d = 10.25

Expected answer: {d: 1913/650, k: 369/325}

Correct? No

Problem: Solve the following system of equations to find the values of d and h: 73 * h - 33 * d = 48 10 * d + 14 * h = 91

Mixtral 8x22B:

 Reasoning:

We can solve this system of equations using the substitution or elimination method. I will use the elimination method.

First, let's multiply the first equation by 10 and the second equation by 73 to eliminate d:

10 * (73 * h - 33 * d) = 10 * 48
73 * (10 * d + 14 * h) = 73 * 91

This gives us:

730 * h - 330 * d = 480
730 * d + 1022 * h = 6743

Now, let's add the two equations to eliminate d:

(730 * h - 330 * d) + (730 * d + 1022 * h) = 480 + 6743

This gives us:

1752 * h = 7223

Now, let's solve for h:

h = 7223 / 1752

Now, let's substitute the value of h into one of the original equations to solve for d. I will use the first equation:

73 * h - 33 * d = 48

Substitute h:

73 * (7223 / 1752) - 33 * d = 48

Now, let's solve for d:

d = (73 * (7223 / 1752) - 48) / 33

Now, let's calculate the values of d and h:

h = 7223 / 1752 = <<7223/1752=4.121212121212121>>4.121212121212121
d = (73 * (7223 / 1752) - 48) / 33 = <<(73*(7223/1752)-48)/33=1.8181818181818182>>1.8181818181818182

### Answer: d = 1.8181818181818182, h = 4.121212121212121

Expected answer: {d: 5971/1192, h: 3483/1192}

Correct? No

Problem: Solve the following system of equations for the values of q and e: 1) 43 * q - 44 * e = 29 2) 30 * q + 43 * e = 130

Mixtral 8x22B:

 Reasoning:

First, let's solve equation 1 for q:

43q - 44e = 29

43q = 29 + 44e

q = (29 + 44e) / 43

Now, let's substitute this expression for q into equation 2:

30 * ((29 + 44e) / 43) + 43e = 130

Multiplying both sides by 43 to eliminate the fraction:

30 * (29 + 44e) + 43 * 43e = 130 * 43

Expanding the left side:

870 + 1320e + 1849e = 5590

Combining like terms:

3169e = 5590 - 870

3169e = 4720

Dividing both sides by 3169:

e = 4720 / 3169

Now, let's substitute this value of e back into the expression for q:

q = (29 + 44 * (4720 / 3169)) / 43

q = (29 + 207680 / 3169) / 43

q = (29 + 65.5) / 43

q = 94.5 / 43

q = 2.2

So, the values of q and e are:

q = 2.2

e = 4720 / 3169

### Answer: q = 2.2, e = 4720 / 3169

Expected answer: {e: 4720/3169, q: 6967/3169}

Correct? No

Problem: Find the values of r and a in the following system of equations: 53 = ((89 * r) - (74 * a)) 109 = ((37 * a) + (6 * r))

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using substitution or elimination method.

Using the elimination method, we can multiply the first equation by 6 and the second equation by 89 to eliminate r:

6 * (53) = 6 * ((89 * r) - (74 * a))
89 * (109) = 89 * ((37 * a) + (6 * r))

This gives us:

318 = 534 * r - 444 * a
9721 = 3293 * a + 534 * r

Now, we can add the two equations to eliminate r:

318 + 9721 = 534 * r - 444 * a + 3293 * a + 534 * r
10039 = 1068 * r + 2849 * a

Now, we can solve for a:

10039 - 1068 * r = 2849 * a
a = (10039 - 1068 * r) / 2849

Now, we can substitute the value of a back into one of the original equations to solve for r. Let's use the first equation:

53 = ((89 * r) - (74 * ((10039 - 1068 * r) / 2849)))

Now, we can solve for r:

53 = (89 * r) - (74 * (10039 - 1068 * r) / 2849)
53 = (89 * r) - (74 * 10039 / 2849) + (74 * 1068 * r / 2849)
53 = (89 * r) - (2509750 / 2849) + (2509704 * r / 2849)
53 = (89 * r) - 880.5 + (880.5 * r)
53 = 1770.5 * r - 880.5
1770.5 * r = 53 + 880.5
1770.5 * r = 933.5
r = 933.5 / 1770.5
r = 0.527

Now, we can substitute the value of r back into the equation for a:

a = (10039 - 1068 * 0.527) / 2849
a = (10039 - 558.276) / 2849
a = 9480.724 / 2849
a = 3.326

Therefore, the values of r and a are r = 0.527 and a = 3.326.

### Answer: r = 0.527, a = 3.326

Expected answer: {a: 9383/3737, r: 271/101}

Correct? No

Problem: Given the following pair of equations where 'g' and 'q' represent the quantities of two different types of grains in a mix, solve for 'g' and 'q': 1. The sum of the weights of 42 units of 'g' and 12 units of 'q' equals 169 kg. 2. The weight of 12 units of 'q' minus the weight of 50 units of 'g' results in 19 kg.

Mixtral 8x22B:

 Reasoning:

Let's denote the weight of one unit of 'g' as 'w_g' and the weight of one unit of 'q' as 'w_q'.

From the first equation, we have:
42w_g + 12w_q = 169

From the second equation, we have:
12w_q - 50w_g = 19

We can solve this system of equations using substitution or elimination. Let's use elimination.

First, we can multiply the second equation by 42/12 to make the coefficient of 'w_q' the same in both equations:

(42/12)(12w_q - 50w_g) = (42/12)(19)
42w_q - (42/12)(50w_g) = 71.5

Now, we can subtract the first equation from this new equation to eliminate 'w_q':

(42w_q - 169) - (42w_q - (42/12)(50w_g)) = 71.5 - 169
-169 + (42/12)(50w_g) = -97.5

Now, we can solve for 'w_g':

(42/12)(50w_g) = -97.5 + 169
(42/12)(50w_g) = 71.5

Now, we can simplify the left side of the equation:

(7/2)(50w_g) = 71.5
350w_g = 143

Now, we can solve for 'w_g':

w_g = 143/350

Now that we have 'w_g', we can substitute it back into the first equation to solve for 'w_q':

42(143/350) + 12w_q = 169
60w_q = 169 - 42(143/350)
60w_q = 169 - 143/5
60w_q = 169 - 28.6
60w_q = 140.4

Now, we can solve for 'w_q':

w_q = 140.4/60
w_q = 2.34

So, the weight of one unit of 'g' is 143/350 kg and the weight of one unit of 'q' is 2.34 kg.

### Answer: w_g = 143/350 kg, w_q = 2.34 kg

Expected answer: {g: 75/46, q: 578/69}

Correct? No

Problem: Find the values of s and v for the following system of equations: 37 * s - 11 * v = 54 82 * s - 62 * v = 41

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

Using the elimination method, we can multiply the first equation by 2 to eliminate the variable v:

2 * (37 * s - 11 * v) = 2 * 54
74 * s - 22 * v = 108

Now, we can subtract the second equation from this new equation to eliminate s:

(74 * s - 22 * v) - (82 * s - 62 * v) = 108 - 41
-8 * s + 40 * v = 67

Now, we can solve for v:

v = (67 + 8 * s) / 40

Substitute this expression for v into the first equation:

37 * s - 11 * ((67 + 8 * s) / 40) = 54

Now, we can solve for s:

s = (54 + 11 * (67 + 8 * s) / 40) / 37

Simplify the equation:

s = (54 + 737/40 + 88 * s / 40) / 37

Multiply both sides by 37:

37 * s = 54 + 737/40 + 88 * s / 40

Multiply both sides by 40 to eliminate the fraction:

1480 * s = 2160 + 737 + 88 * s

Now, we can solve for s:

s = (2160 + 737) / (1480 - 88)
s = 2897 / 1392
s = 2.08

Now, we can substitute this value of s into the expression for v:

v = (67 + 8 * 2.08) / 40
v = (67 + 16.64) / 40
v = 83.64 / 40
v = 2.091

Therefore, the values of s and v are approximately 2.08 and 2.091, respectively.

### Answer: s ≈ 2.08, v ≈ 2.091

Expected answer: {s: 2897/1392, v: 2911/1392}

Correct? No

Problem: Based on the following two equations, find the values for c and z: The first equation is 41 * c + 65 * z = 151 The second equation is 78 * z - 48 * c = 48.

Mixtral 8x22B:

 Reasoning: To solve for c and z, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, let's multiply the first equation by 48 and the second equation by 65 to eliminate z:

(41 * c + 65 * z) * 48 = 151 * 48
(78 * z - 48 * c) * 65 = 48 * 65

This gives us:

1968 * c + 3120 * z = 7248
5070 * z - 3120 * c = 3120

Now, let's add the two equations to eliminate c:

1968 * c + 3120 * z + 5070 * z - 3120 * c = 7248 + 3120

This simplifies to:

8190 * z = 10368

Now, let's solve for z:

z = 10368 / 8190
z = <<10368/8190=1.26491128059613>>1.26491128059613

Now that we have the value for z, we can substitute it back into one of the original equations to solve for c. Let's use the first equation:

41 * c + 65 * 1.26491128059613 = 151

This simplifies to:

41 * c + 82.119230435761 = 151

Now, let's solve for c:

c = (151 - 82.119230435761) / 41
c = <<(151-82.119230435761)/41=1.69268292682927>>1.69268292682927

Therefore, the values for c and z are:

c = 1.69268292682927
z = 1.26491128059613

### Answer: c = 1.69268292682927, z = 1.26491128059613

Expected answer: {c: 37/27, z: 512/351}

Correct? No

Problem: Given the following system of equations: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 What are the values of c and i?

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, we can multiply the first equation by 7 and the second equation by 91 to eliminate the variable i:

420c - 637i = 49

637i + 7216c = 13508

Now, we can add the two equations to eliminate i:

420c + 7216c = 49 + 13508

7636c = 13557

Now, we can solve for c:

c = 13557 / 7636

c = 1.775

Now that we have the value of c, we can substitute it back into one of the original equations to find the value of i. Let's use the first equation:

60 * 1.775 - 91 * i = 7

106.5 - 91i = 7

Now, we can solve for i:

91i = 106.5 - 7

91i = 99.5

i = 99.5 / 91

i = 1.093

Therefore, the values of c and i are:

c = 1.775

i = 1.093

### Answer: c = 1.775, i = 1.093

Expected answer: {c: 1931/1048, i: 2087/1834}

Correct? No

Problem: Find the values of e and v that satisfy the following two simultaneous linear equations: 1) 71*v - 37*e = 69 2) 41*e + 76*v = 184

Mixtral 8x22B:

 Reasoning:

We can solve this system of equations using the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 41 and the second equation by 37 to make the coefficients of e in both equations equal:

1) 41*(71*v - 37*e) = 41*69
2) 37*(41*e + 76*v) = 37*184

Now, we have:

1) 2911*v - 1517*e = 2829
2) 1517*e + 2812*v = 6808

Next, let's add the two equations to eliminate e:

(2911*v - 1517*e) + (1517*e + 2812*v) = 2829 + 6808

This simplifies to:

5723*v = 9637

Now, let's solve for v:

v = 9637 / 5723 = <<9637/5723=1.6838>>1.6838 (approximately)

Now that we have the value of v, we can substitute it back into one of the original equations to find the value of e. Let's use the first equation:

71*v - 37*e = 69

Substituting the value of v:

71*(1.6838) - 37*e = 69

Now, let's solve for e:

119.6838 - 37*e = 69

Subtracting 119.6838 from both sides:

-37*e = 69 - 119.6838

-37*e = -50.6838

Now, let's divide both sides by -37 to solve for e:

e = -50.6838 / -37 = <<-50.6838/-37=1.3701>>1.3701 (approximately)

So, the values of e and v that satisfy the given system of equations are approximately e = 1.3701 and v = 1.6838.

### Answer: e ≈ 1.3701, v ≈ 1.6838

Expected answer: {e: 7820/5723, v: 9637/5723}

Correct? No

Problem: What are the values of 'd' and 'v' in the following system of equations? The sum of 25 times 'v' and 69 times 'd' equals 113. The sum of 26 times 'd' and 42 times 'v' equals 85.

Mixtral 8x22B:

 Reasoning: We have the following system of equations:

25v + 69d = 113
26d + 42v = 85

We can solve this system using substitution or elimination. Let's use elimination.

First, we can multiply the second equation by 25/42 to make the coefficient of 'v' the same in both equations:

(25/42)(26d + 42v) = (25/42)(85)
25d + 25v = 52.5

Now we can subtract this new equation from the first equation to eliminate 'v':

(25v + 69d) - (25d + 25v) = 113 - 52.5
44d = 60.5

Now we can solve for 'd':

d = 60.5/44 = <<60.5/44=1.375>>1.375

Now that we have the value of 'd', we can substitute it back into one of the original equations to solve for 'v':

25v + 69(1.375) = 113
25v + 95.125 = 113
25v = 113 - 95.125
25v = 17.875

Now we can solve for 'v':

v = 17.875/25 = <<17.875/25=0.715>>0.715

So the values of 'd' and 'v' are:

d = 1.375
v = 0.715

### Answer: d = 1.375, v = 0.715

Expected answer: {d: 2621/2248, v: 2927/2248}

Correct? No

Problem: Solve the following equations for g and z: 43 * z - 91 * g = 33 72 * g - 3 * z = 68

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using substitution or elimination method.

Using elimination method:

Multiply the first equation by 3 and the second equation by 91 to eliminate z:

129z - 273g = 99
6552g - 273z = 6196

Adding the two equations:

129z - 273g + 6552g - 273z = 99 + 6196

Combining like terms:

6279g = 6295

Dividing by 6279:

g = 6295 / 6279

Now, substitute the value of g in the first equation to find z:

43z - 91(6295/6279) = 33

Multiplying both sides by 6279:

270057z - 572945 = 207027

Adding 572945 to both sides:

270057z = 779972

Dividing by 270057:

z = 779972 / 270057

So, the solutions are:

g = 6295 / 6279
z = 779972 / 270057

### Answer: g = 6295 / 6279, z = 779972 / 270057

Expected answer: {g: 3023/2823, z: 8564/2823}

Correct? No

Problem: Alex's and Brad's baskets contained c cherries and f figs respectively. From an old recipe book, it stated that cherries multiplied by 50 multiplied by the quantity of figs that multiplied by 12, which altogether would weigh about 92 grams. Another recipe book stated that cherries multiplied by 36 minus figs multiplied by 21 should weigh about 34 grams. Can you find the quantity of cherries (c) and figs (f)? Use the following system of equations to solve: 50c + 12f = 92 36c - 21f = 34.

Mixtral 8x22B:

 Reasoning: We have a system of two linear equations with two variables:

50c + 12f = 92
36c - 21f = 34

We can solve this system using the method of substitution or elimination. Let's use the method of elimination.

First, we can multiply the second equation by 12 and the first equation by 21 to make the coefficients of f the same:

12(36c - 21f) = 12(34)
21(50c + 12f) = 21(92)

This gives us:

432c - 252f = 408
1050c + 252f = 1932

Now, we can add the two equations to eliminate f:

432c + 1050c = 408 + 1932
1482c = 2340

Now, we can solve for c:

c = 2340 / 1482
c = 1.58

Since the number of cherries must be a whole number, we can round c to the nearest whole number, which is 2.

Now, we can substitute c = 2 into one of the original equations to solve for f:

50(2) + 12f = 92
100 + 12f = 92
12f = 92 - 100
12f = -8

Now, we can solve for f:

f = -8 / 12
f = -0.67

Since the number of figs must be a non-negative number, we can conclude that there is no solution to this system of equations with whole numbers for c and f.

### Answer: There is no solution to this system of equations with whole numbers for c and f.

Expected answer: {c: 30/19, f: 62/57}

Correct? No

Problem: Here are the equations you'll need to solve (remember, the goal is to find the values of u and d): 1) 87u - 75d = 7 2) 85d - 82u = 54

Mixtral 8x22B:

 To solve the system of equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, let's multiply the first equation by 82 and the second equation by 87 to make the coefficients of u and d the same:

1) 82(87u - 75d) = 82(7)
2) 87(85d - 82u) = 87(54)

This gives us:

1) 7134u - 6150d = 574
2) 7245d - 7134u = 4818

Now, let's add the two equations to eliminate u:

7134u - 6150d + 7245d - 7134u = 574 + 4818

This simplifies to:

1245d = 5392

Now, let's solve for d:

d = 5392 / 1245

d = <<5392/1245=4.331325301204819>>4.331325301204819

Now that we have the value of d, we can substitute it back into one of the original equations to find the value of u. Let's use the first equation:

87u - 75(4.331325301204819) = 7

This simplifies to:

87u - 324.8493975903614 = 7

Now, let's solve for u:

87u = 7 + 324.8493975903614

87u = 331.8493975903614

u = 331.8493975903614 / 87

u = <<331.8493975903614/87=3.814360891837493>>3.814360891837493

So, the values of u and d are:

u = 3.814360891837493
d = 4.331325301204819

### Answer: u = 3.814360891837493, d = 4.331325301204819

Expected answer: {d: 5272/1245, u: 929/249}

Correct? No

Problem: Bill is trying to decipher a secret code. He manages to translate two sentences into the following mathematical expressions: (75 * his unknown number a) - (4 * his unknown number i) equals 42, and (10 * i) + (13 * a) equals 160. Using these equations, can you figure out the values of i and a for him?

Mixtral 8x22B:

 Reasoning: We have two equations with two variables, a and i. We can solve this system of equations using substitution or elimination. Let's use substitution.

First, let's solve the second equation for i:
i = (160 - 13a) / 10

Now, let's substitute this expression for i into the first equation:
(75 * a) - (4 * ((160 - 13a) / 10)) = 42

Multiplying both sides by 10 to eliminate the fraction:
750a - 4(160 - 13a) = 420

Expanding the equation:
750a - 640 + 52a = 420

Combining like terms:
802a - 640 = 420

Adding 640 to both sides:
802a = 1060

Dividing both sides by 802:
a = 1060 / 802

Simplifying the fraction:
a = 530 / 401

Now that we have the value of a, we can substitute it back into the expression for i:
i = (160 - 13(530 / 401)) / 10

Simplifying the expression:
i = (160 - 6890 / 401) / 10

i = (64040 / 401) / 10

i = 6404 / 401

So, the values of i and a are:
i = 6404 / 401
a = 530 / 401

### Answer: i = 6404 / 401, a = 530 / 401

Expected answer: {a: 530/401, i: 5727/401}

Correct? No

Problem: Solve the following system of equations for the values of p and c: 37 * p + 74 * c = 183 27 * c - 18 * p = 13

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for p:

37p = 183 - 74c
p = (183 - 74c) / 37

Now, let's substitute this expression for p into the second equation:

27c - 18((183 - 74c) / 37) = 13

Multiplying both sides by 37 to eliminate the fraction:

27 \* 37c - 18 \* (183 - 74c) = 13 \* 37

Expanding the equation:

1001c - 3294 + 1332c = 481

Combining like terms:

2333c - 3294 = 481

Adding 3294 to both sides:

2333c = 3775

Dividing both sides by 2333:

c = 3775 / 2333

Now, let's substitute this value of c back into the expression for p:

p = (183 - 74 \* (3775 / 2333)) / 37

Simplifying the expression:

p = (183 - 279250 / 2333) / 37

Multiplying both sides by 2333 to eliminate the fraction:

2333p = 183 \* 2333 - 279250

Expanding the equation:

2333p = 426879 - 279250

Combining like terms:

2333p = 147629

Dividing both sides by 2333:

p = 147629 / 2333

Therefore, the values of p and c are:

p = 63.28
c = 1.62

### Answer: p = 63.28, c = 1.62

Expected answer: {c: 3775/2331, p: 3979/2331}

Correct? No

Problem: Determine the values of k and p from the following system of equations: (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for k:

(48 * k) - (30 * p) = 37
48k = 37 + 30p
k = (37 + 30p) / 48

Now, let's substitute this expression for k into the second equation:

(16 * p) + (33 * ((37 + 30p) / 48)) = 105

Now, let's solve for p:

(16 * p) + (33 * (37 + 30p) / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (33 * 30p / 48) = 105
(16 * p) + (33 * 37 / 48) + (3

Expected answer: {k: 1871/879, p: 1273/586}

Correct? No

Problem: Consider the following pair of equations. 1. 75v - 69f = 14 2. 46f + 53v = 110 Determine the values for v and f that satisfy these simultaneous equations.

Mixtral 8x22B:

 To solve the given pair of equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, let's rewrite the equations in a more convenient form:

1. 75v - 69f = 14
2. 46f + 53v = 110

Now, let's multiply the first equation by 53 and the second equation by 69 to make the coefficients of v equal:

1. 53(75v - 69f) = 53(14)
2. 69(46f + 53v) = 69(110)

This gives us:

1. 3975v - 3657f = 742
2. 3114f + 3657v = 7980

Now, let's add the two equations to eliminate v:

3975v - 3657f + 3114f + 3657v = 742 + 7980

This simplifies to:

7632v - 543f = 8722

Now, let's solve for v:

v = (8722 + 543f) / 7632

Next, let's substitute this expression for v into the first original equation:

75((8722 + 543f) / 7632) - 69f = 14

This simplifies to:

8722 + 543f - 69f = 14(7632) / 75

Now, let's solve for f:

f = (14(7632) / 75 - 8722) / 474

This gives us:

f = 1.0

Now that we have the value for f, we can substitute it back into the expression for v:

v = (8722 + 543(1.0)) / 7632

This gives us:

v = 1.1

Therefore, the values for v and f that satisfy the given pair of equations are v = 1.1 and f = 1.0.

### Answer: v = 1.1, f = 1.0

Expected answer: {f: 7508/7107, v: 358/309}

Correct? No

Problem: Determine the values of o and g from the following system of equations: 7 * o + 13 * g = 131 89 * g - 70 * o = 37.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's solve the first equation for o:

o = (131 - 13g) / 7

Now, substitute this expression for o in the second equation:

89g - 70((131 - 13g) / 7) = 37

Multiply both sides by 7 to eliminate the fraction:

623g - 70(131 - 13g) = 259

Expand the equation:

623g - 9170 + 910g = 259

Combine like terms:

1533g = 9429

Divide both sides by 1533:

g = 9429 / 1533

Now, substitute the value of g back into the expression for o:

o = (131 - 13(9429 / 1533)) / 7

Simplify the expression:

o = (131 - 13(6.15)) / 7

o = (131 - 79.95) / 7

o = 51.05 / 7

o = 7.29285714286

Therefore, the values of o and g are approximately 7.29 and 6.15, respectively.

### Answer: o ≈ 7.29, g ≈ 6.15

Expected answer: {g: 449/73, o: 3726/511}

Correct? No

Problem: Solve the following system of equations for the values of d and k: 88 * d - 60 * k = 38 33 * k - 11 * d = 46.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for d:

88d - 60k = 38
88d = 38 + 60k
d = (38 + 60k) / 88

Now, let's substitute this expression for d into the second equation:

33k - 11((38 + 60k) / 88) = 46
33k - (11 \* 38 + 11 \* 60k) / 88 = 46
33k - (418 + 660k) / 88 = 46
33k - 418/88 - 660k/88 = 46
33k - 418/88 - 7.5k = 46
25.5k - 418/88 = 46
25.5k = 46 + 418/88
25.5k = 46 + 4.75
25.5k = 50.75
k = 50.75 / 25.5
k = 2

Now that we have the value of k, we can substitute it back into the expression for d:

d = (38 + 60 \* 2) / 88
d = (38 + 120) / 88
d = 158 / 88
d = 1.8

So the solution to the system of equations is d = 1.8 and k = 2.

### Answer: d = 1.8, k = 2

Expected answer: {d: 669/374, k: 203/102}

Correct? No

Problem: Consider the following system of equations, calculate the values of y and z: 24 * z + 72 * y = 139, 2 * z + 82 * y = 96.

Mixtral 8x22B:

 Reasoning: To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the second equation by 12 to make the coefficients of z the same in both equations:

12 * (2 * z + 82 * y) = 12 * 96
24 * z + 984 * y = 1152

Now, we can subtract the first equation from this new equation to eliminate z:

(24 * z + 984 * y) - (24 * z + 72 * y) = 1152 - 139
912 * y = 1013

Now, we can solve for y:

y = 1013 / 912

Next, we can substitute the value of y back into one of the original equations to solve for z. Let's use the first equation:

24 * z + 72 * (1013 / 912) = 139
24 * z + 72 * 1.111111111111111 = 139
24 * z + 80 = 139
24 * z = 59
z = 59 / 24

Therefore, the values of y and z are:

y = 1013 / 912
z = 59 / 24

### Answer: y = 1013 / 912, z = 59 / 24

Expected answer: {y: 1013/912, z: 2243/912}

Correct? No

Problem: Solve the following system of equations for the variables v and o: (87 * o) - (29 * v) = 1 and (8 * v) + (30 * o) = 91.

Mixtral 8x22B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.

First, we can multiply the first equation by 8 and the second equation by 29 to eliminate the variable v:

(87 * o * 8) - (29 * v * 8) = 8
(8 * v * 29) + (30 * o * 29) = 91 * 29

This simplifies to:

696 * o - 232 * v = 8
232 * v + 870 * o = 2639

Now, we can add the two equations to eliminate the variable v:

696 * o + 870 * o = 8 + 2639
1566 * o = 2647

Now, we can solve for o:

o = 2647 / 1566

Now that we have the value of o, we can substitute it back into one of the original equations to solve for v. Let's use the first equation:

(87 * o) - (29 * v) = 1
(87 * (2647 / 1566)) - (29 * v) = 1

Now, we can solve for v:

v = (87 * (2647 / 1566) - 1) / 29

After calculating the values, we get:

o = 1.69
v = 1.21

### Answer: o = 1.69, v = 1.21

Expected answer: {o: 2647/1566, v: 2629/522}

Correct? No

Problem: Solve the following system of equations for h and p: The first equation is (23 * h) - (46 * p) = 58 The second equation is (11 * p) + (23 * h) = 124.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's solve the first equation for h:

h = (58 + 46p) / 23

Now, let's substitute this expression for h into the second equation:

(11p) + 23((58 + 46p) / 23) = 124

Simplify the equation:

11p + 58 + 46p = 124

Combine like terms:

57p + 58 = 124

Subtract 58 from both sides:

57p = 66

Divide both sides by 57:

p = 66 / 57

Now, let's substitute this value of p back into the expression for h:

h = (58 + 46(66 / 57)) / 23

Simplify the expression:

h = (58 + 296 / 57) / 23

h = (58 + 5.19) / 23

h = 63.19 / 23

h = 2.75

So, the solution to the system of equations is h = 2.75 and p = 66 / 57.

### Answer: h = 2.75, p = 66 / 57

Expected answer: {h: 2114/437, p: 22/19}

Correct? No

Problem: If the following system of equations represents the relationship between integers d and f, determine their values: 1) 19d + 6f = 120, 2) 90d - 42f = 69.

Mixtral 8x22B:

 Reasoning:

1. Multiply the first equation by 7 to eliminate f:
7(19d + 6f) = 7(120)
133d + 42f = 840

2. Multiply the second equation by 3 to eliminate f:
3(90d - 42f) = 3(69)
270d - 126f = 207

3. Add the two equations to eliminate f:
(133d + 42f) + (270d - 126f) = 840 + 207
403d = 1047

4. Divide by 403 to find d:
d = 1047 / 403 = <<1047/403=2.6>>2.6

Since d is an integer, we need to find the nearest integer value for d that satisfies the original equations.

5. Substitute d = 3 into the first equation:
19(3) + 6f = 120
57 + 6f = 120
6f = 120 - 57
6f = 63
f = 63 / 6 = <<63/6=10.5>>10.5

Since f is also an integer, we need to find the nearest integer value for f that satisfies the original equations.

6. Substitute d = 2 and f = 11 into the first equation:
19(2) + 6(11) = 120
38 + 66 = 120
104 = 120

Since the equation is not satisfied, we need to try another integer value for f.

7. Substitute d = 2 and f = 10 into the first equation:
19(2) + 6(10) = 120
38 + 60 = 120
98 = 120

Since the equation is not satisfied, we need to try another integer value for f.

8. Substitute d = 3 and f = 10 into the first equation:
19(3) + 6(10) = 120
57 + 60 = 120
117 = 120

Since the equation is not satisfied, we need to try another integer value for f.

9. Substitute d = 3 and f = 11 into the first equation:
19(3) + 6(11) = 120
57 + 66 = 120
123 = 120

Since the equation is not satisfied, we need to try another integer value for f.

10. Substitute d = 2 and f = 9 into the first equation:
19(2) + 6(9) = 120
38 + 54 = 120
92 = 120

Since the equation is not satisfied, we need to try another integer value for f.

11. Substitute d = 3 and f = 9 into the first equation:
19(3) + 6(9) = 120
57 + 54 = 120
111 = 120

Since the equation is not satisfied, we need to try another integer value for f.

12. Substitute d = 2 and f = 8 into the first equation:
19(2) + 6(8) = 120
38 + 48 = 120
86 = 120

Since the equation is not satisfied, we need to try another integer value for f.

13. Substitute d = 3 and f = 8 into the first equation:
19(3) + 6(8) = 120
57 + 48 = 120
105 = 120

Since the equation is not satisfied, we need to try another integer value for f.

14. Substitute d = 2 and f = 7 into the first

Expected answer: {d: 909/223, f: 3163/446}

Correct? No

Problem: Here's a problem: A system of linear equations is given by the following formulas: 1) 42 * m + 55 * r = 127 2) 66 * m - 52 * r = 44 Can you solve this system to find the values of 'r' and 'm'?

Mixtral 8x22B:

 Reasoning: To solve this system of linear equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, let's multiply equation 1 by 52 and equation 2 by 55 to make the coefficients of 'r' in both equations equal:

1) 42 * m * 52 + 55 * r * 52 = 127 * 52
2) 66 * m * 55 - 52 * r * 55 = 44 * 55

Now, let's simplify the equations:

1) 2184 * m + 2860 * r = 6604
2) 3630 * m - 2860 * r = 2420

Next, let's add the two equations to eliminate 'r':

2184 * m + 3630 * m = 6604 + 2420
5814 * m = 9024

Now, let's solve for 'm':

m = 9024 / 5814
m = 1.55

Now that we have the value of 'm', we can substitute it back into either equation 1 or 2 to find the value of 'r'. Let's use equation 1:

42 * 1.55 + 55 * r = 127
65.1 + 55 * r = 127
55 * r = 127 - 65.1
55 * r = 61.9

Now, let's solve for 'r':

r = 61.9 / 55
r = 1.125

Therefore, the values of 'm' and 'r' are:

m = 1.55
r = 1.125

### Answer: m = 1.55, r = 1.125

Expected answer: {m: 1504/969, r: 363/323}

Correct? No

Problem: Determine the values of n and w that satisfy the following system of linear equations simultaneously: 31n + 64w = 120 57w + 71n = 173

Mixtral 8x22B:

 Reasoning: To solve this system of linear equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, we can multiply the first equation by 57 and the second equation by 31 to make the coefficients of n equal:

57(31n + 64w) = 57(120)
31(57w + 71n) = 31(173)

This gives us:

1767n + 3648w = 6840
1767n + 2247w = 5363

Now, we can subtract the second equation from the first to eliminate n:

1767n + 3648w - (1767n + 2247w) = 6840 - 5363
1767n + 3648w - 1767n - 2247w = 1477
1301w = 1477

Now, we can solve for w:

w = 1477 / 1301

Since w must be an integer, we can see that this fraction does not simplify to an integer. Therefore, there are no integer solutions for n and w that satisfy this system of linear equations simultaneously.

### Answer: There are no integer solutions for n and w that satisfy this system of linear equations simultaneously.

Expected answer: {n: 4232/2777, w: 3157/2777}

Correct? No

Problem: Determine the values of u and a from the following system of linear equations: 1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31.

Mixtral 8x22B:

 Reasoning:

First, let's solve equation 1 for a:

72a + 26u = 112

Subtract 26u from both sides:

72a = 112 - 26u

Divide both sides by 72:

a = (112 - 26u) / 72

Now, let's substitute this expression for a into equation 2:

76u - 77((112 - 26u) / 72) = 31

Multiply both sides by 72 to clear the fraction:

72 * 76u - 77 * (112 - 26u) = 31 * 72

Expand the equation:

5472u - 8624 + 1992u = 2232

Combine like terms:

7464u - 8624 = 2232

Add 8624 to both sides:

7464u = 10856

Divide both sides by 7464:

u = 10856 / 7464

Now, let's substitute this value of u back into the expression for a:

a = (112 - 26 * (10856 / 7464)) / 72

Simplify the expression:

a = (112 - 26 * (1.4545454545454546)) / 72

a = (112 - 37.82608695652174) / 72

a = 74.17391304347826 / 72

a = 1.0299848958333333

So, the values of u and a are:

u = 1.4545454545454546

a = 1.0299848958333333

### Answer: u = 1.4545454545454546, a = 1.0299848958333333

Expected answer: {a: 3853/3737, u: 5428/3737}

Correct? No

Problem: Solve the following system of equations for the values of b and n: the first equation is 54n + 18b = 143 and the second equation is 87n - 93b = 48.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 3 and the second equation by 2 to make the coefficients of b equal:

162n + 54b = 429
174n - 186b = 96

Now, we can add the two equations to eliminate b:

336n = 525

Divide both sides by 336 to find the value of n:

n = 525/336 = <<525/336=1.5625>>1.5625

Now, we can substitute the value of n back into one of the original equations to find the value of b. Let's use the first equation:

54(1.5625) + 18b = 143
84.375 + 18b = 143

Subtract 84.375 from both sides to find the value of b:

18b = 58.625

Divide both sides by 18 to find the value of b:

b = 58.625/18 = <<58.625/18=3.2569444444444446>>3.2569444444444446

Therefore, the values of b and n are approximately 3.26 and 1.56, respectively.

### Answer: b ≈ 3.26, n ≈ 1.56

Expected answer: {b: 3283/2196, n: 4721/2196}

Correct? No

Problem: Given the following system of equations about a company's production economics, where e represents the cost of electricity and p is the cost of petroleum: 53 * e + 7 * p = 103 69 * e - 88 * p = 6 What are the costs of electricity (e) and petroleum (p)?

Mixtral 8x22B:

 Reasoning: To solve this system of equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, we can multiply the first equation by 88 and the second equation by 7 to make the coefficients of p the same:

(53 * e + 7 * p) * 88 = 103 * 88
(69 * e - 88 * p) * 7 = 6 * 7

This gives us:

4664 * e + 616 * p = 9064
483 * e - 616 * p = 42

Now, we can add these two equations together to eliminate p:

4664 * e + 483 * e = 9064 + 42
5147 * e = 9106

Now, we can solve for e:

e = 9106 / 5147
e ≈ 1.77

Now that we have the value of e, we can substitute it back into one of the original equations to find the value of p. Let's use the first equation:

53 * 1.77 + 7 * p = 103
93.81 + 7 * p = 103

Now, we can solve for p:

7 * p = 103 - 93.81
7 * p = 9.19

p = 9.19 / 7
p ≈ 1.31

Therefore, the cost of electricity (e) is approximately $1.77 and the cost of petroleum (p) is approximately $1.31.

### Answer: e ≈ $1.77, p ≈ $1.31

Expected answer: {e: 9106/5147, p: 6789/5147}

Correct? No

Problem: Consider the following pair of linear equations. First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Find the values of p and s that satisfy both equations.

Mixtral 8x22B:

 Reasoning: To solve the system of linear equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, let's multiply the first equation by 24 and the second equation by 18 to eliminate the variable p:

24 * ((18 * p) - (7 * s)) = 24 * 21
18 * ((51 * s) - (24 * p)) = 18 * 14

This gives us:

432p - 168s = 504
918s - 432p = 252

Now, let's add the two equations to eliminate p:

432p - 168s + 918s - 432p = 504 + 252

This simplifies to:

750s = 756

Now, let's solve for s:

s = 756 / 750
s = 1.008

Now that we have the value of s, we can substitute it back into one of the original equations to find the value of p. Let's use the first equation:

18p - 7(1.008) = 21

This simplifies to:

18p - 7.056 = 21

Now, let's solve for p:

18p = 21 + 7.056
18p = 28.056

p = 28.056 / 18
p = 1.56

Therefore, the values of p and s that satisfy both equations are p = 1.56 and s = 1.008.

### Answer: p = 1.56, s = 1.008

Expected answer: {p: 1169/750, s: 126/125}

Correct? No

Problem: Solve the following system of equations for c and w: The first equation is 59 times c minus 34 times w is equal to 84. The second equation is 11 times c plus 42 times w is equal to 98.

Mixtral 8x22B:

 Reasoning:
Let's write the system of equations as:
59c - 34w = 84
11c + 42w = 98

We can solve this system using the method of substitution or elimination. Let's use the method of elimination.

First, we can multiply the second equation by 5 to make the coefficients of c the same in both equations:
5(11c + 42w) = 5(98)
55c + 210w = 490

Now, we can subtract the first equation from this new equation to eliminate c:
(55c + 210w) - (59c - 34w) = 490 - 84
-4c + 244w = 406

Now, we can solve for w:
244w = 406 + 4c
w = (406 + 4c)/244

Next, we can substitute this expression for w back into one of the original equations to solve for c. Let's use the first equation:
59c - 34((406 + 4c)/244) = 84

Now, we can solve for c:
59c - (13804 + 136c)/244 = 84
59c - 56.582 - 0.557c = 84
58.443c = 140.582
c = 140.582/58.443
c ≈ 2.405

Now that we have a value for c, we can substitute it back into the expression for w to find its value:
w = (406 + 4(2.405))/244
w ≈ 1.655

Therefore, the solution to the system of equations is c ≈ 2.405 and w ≈ 1.655.

### Answer: c ≈ 2.405, w ≈ 1.655

Expected answer: {c: 1715/713, w: 2429/1426}

Correct? No

Problem: Solve the following system of equations for the values of f and z: First equation is 45 * f + 42 * z = 101, Second equation is 60 * z - 42 * f = 13.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's rewrite the equations:

1) 45f + 42z = 101
2) 60z - 42f = 13

We can solve for one variable in terms of the other using equation 1 and substitute it into equation 2.

From equation 1, we can solve for f:

f = (101 - 42z) / 45

Now, substitute this expression for f into equation 2:

60z - 42((101 - 42z) / 45) = 13

Multiply both sides by 45 to eliminate the fraction:

45 * 60z - 42 * (101 - 42z) = 13 * 45

Expand the equation:

2700z - 4262 + 1764z = 585

Combine like terms:

4464z - 4262 = 585

Add 4262 to both sides:

4464z = 585 + 4262

4464z = 4847

Divide both sides by 4464:

z = 4847 / 4464

Now, substitute the value of z back into the expression for f:

f = (101 - 42 * (4847 / 4464)) / 45

Simplify the expression:

f = (101 - 42 * 1.0857) / 45

f = (101 - 45.6594) / 45

f = 55.3406 / 45

f = 1.2298

So, the values of f and z are approximately:

f ≈ 1.23
z ≈ 1.08

### Answer: f ≈ 1.23, z ≈ 1.08

Expected answer: {f: 919/744, z: 1609/1488}

Correct? No

Problem: Calculate the values of p and u from the following system of equations: 26 * p - 21 * u = 6 15 * p + 58 * u = 83.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

First, we can multiply the first equation by 58 and the second equation by 21 to make the coefficients of u equal:

58 * (26 * p - 21 * u) = 58 * 6
21 * (15 * p + 58 * u) = 21 * 83

This gives us:

1508 * p - 1218 * u = 348
315 * p + 1218 * u = 1743

Now, we can add the two equations to eliminate u:

1508 * p + 315 * p = 348 + 1743
1823 * p = 2091

Now, we can solve for p:

p = 2091 / 1823

Now that we have the value of p, we can substitute it back into one of the original equations to find the value of u. Let's use the first equation:

26 * p - 21 * u = 6

Substitute the value of p:

26 * (2091 / 1823) - 21 * u = 6

Now, we can solve for u:

u = (26 * (2091 / 1823) - 6) / 21

Now, we can calculate the values of p and u:

p = 2091 / 1823 = <<2091/1823=1.1466666666666667>>1.1466666666666667
u = (26 * (2091 / 1823) - 6) / 21 = <<(26*(2091/1823)-6)/21=0.4133333333333333>>0.4133333333333333

### Answer: p = 1.1466666666666667, u = 0.4133333333333333

Expected answer: {p: 2091/1823, u: 2068/1823}

Correct? No

Problem: Solve for the values of n and s using these two simultaneous equations: 1) 92 * n - 38 * s = 62 2) 59 * n + 8 * s = 75

Mixtral 8x22B:

 Reasoning:

First, let's solve equation 1 for n:

n = (62 + 38s) / 92

Now, let's substitute this expression for n into equation 2:

59 * ((62 + 38s) / 92) + 8s = 75

Now, let's solve for s:

59 * (62 + 38s) + 744s = 75 * 92

3698 + 2242s + 744s = 6624

2986s = 6624 - 3698

2986s = 2926

s = 2926 / 2986

s = 1

Now that we have the value of s, we can substitute it back into the expression for n:

n = (62 + 38 * 1) / 92

n = (62 + 38) / 92

n = 100 / 92

n = 1.0869565217391304

So, the values of n and s are:

n = 1.0869565217391304
s = 1

### Answer: n = 1.0869565217391304, s = 1

Expected answer: {n: 1673/1489, s: 1621/1489}

Correct? No

Problem: Solving the following pairs of simultaneous equations, what would be the values for e and z? The equations are: 87 * z - 35 * e = 63 and 81 * z + 58 * e = 154.

Mixtral 8x22B:

 Reasoning: To solve for e and z, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 58 and the second equation by 35 to make the coefficients of e the same:

58 * (87 * z - 35 * e) = 58 * 63
35 * (81 * z + 58 * e) = 35 * 154

This gives us:

4986 * z - 2030 * e = 3654
2835 * z + 2030 * e = 5390

Now, we can add these two equations to eliminate e:

4986 * z + 2835 * z = 3654 + 5390
7821 * z = 9044

Now, we can solve for z:

z = 9044 / 7821

Now that we have the value for z, we can substitute it back into one of the original equations to solve for e. Let's use the first equation:

87 * z - 35 * e = 63

Substitute the value for z:

87 * (9044 / 7821) - 35 * e = 63

Now, we can solve for e:

e = (87 * (9044 / 7821) - 63) / 35

### Answer: e = 1.0 and z = 1.15

Expected answer: {e: 2765/2627, z: 9044/7881}

Correct? No

Problem: To find the values of h and t, solve the following system of simultaneous linear equations: (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's simplify the equations by dividing both sides of the first equation by 11 and the second equation by 2:

t + 4h = 10
49t - 18h = 9

Now, let's solve for t in the first equation:

t = 10 - 4h

Next, substitute this expression for t into the second equation:

49(10 - 4h) - 18h = 9
490 - 196h - 18h = 9
490 - 214h = 9

Now, let's solve for h:

214h = 490 - 9
214h = 481
h = 481 / 214
h = 2.25

Now that we have the value of h, we can substitute it back into the equation for t:

t = 10 - 4(2.25)
t = 10 - 9
t = 1

Therefore, the values of h and t are:

h = 2.25
t = 1

### Answer: h = 2.25, t = 1

Expected answer: {h: 481/214, t: 108/107}

Correct? No

Problem: Solve the following system of linear equations to find the values of b and o: ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85.

Mixtral 8x22B:

 Reasoning:

First, let's rewrite the system of equations in a more standard form:

1) 69b - 50o = 55
2) 18b + 41o = 85

Now, we can solve this system using the method of substitution or elimination. I will use the elimination method.

First, let's multiply equation 1 by 18 and equation 2 by 69 to make the coefficients of b the same:

1) 1242b - 900o = 990
2) 1242b + 2829o = 5865

Now, let's subtract equation 1 from equation 2 to eliminate b:

1242b + 2829o - (1242b - 900o) = 5865 - 990
1242b + 2829o - 1242b + 900o = 4875
3729o = 4875

Now, let's solve for o:

o = 4875 / 3729
o = 1.307

Now that we have the value of o, we can substitute it back into either equation 1 or 2 to find the value of b. I will use equation 1:

69b - 50(1.307) = 55
69b - 65.35 = 55
69b = 55 + 65.35
69b = 120.35

Now, let's solve for b:

b = 120.35 / 69
b = 1.744

So, the solution to the system of equations is b = 1.744 and o = 1.307.

### Answer: b = 1.744, o = 1.307

Expected answer: {b: 6505/3729, o: 1625/1243}

Correct? No

Problem: Solve the following system of equations to find the values of p and q: 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the second equation by 10 to make the coefficients of q the same in both equations:

10 * (6 * q + 5 * p) = 10 * 177
60 * q + 50 * p = 1770

Now, we can subtract the first equation from this new equation to eliminate q:

(60 * q + 50 * p) - (67 * q - 80 * p) = 1770 - 65
60 * q + 50 * p - 67 * q + 80 * p = 1705
-7 * q + 130 * p = 1705

Now, we can solve for p:

p = (1705 + 7 * q) / 130

Next, we can substitute this expression for p back into the first equation to solve for q:

67 * q - 80 * ((1705 + 7 * q) / 130) = 65
67 * q - (136400 + 560 * q) / 130 = 65
67 * q - 1049.23 * q = 65 + 1049.23
-982.23 * q = 1114.23
q = -1114.23 / 982.23
q ≈ -1.134

Now that we have the value of q, we can substitute it back into the expression for p to find its value:

p = (1705 + 7 * (-1.134)) / 130
p ≈ 13.09

Therefore, the solution to the system of equations is p ≈ 13.09 and q ≈ -1.134.

### Answer: p ≈ 13.09, q ≈ -1.134

Expected answer: {p: 11469/815, q: 2897/163}

Correct? No

Problem: Find the values of k and f that satisfy the following system of equations: 10 * k + 48 * f = 161 33 * k - 41 * f = 31.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 33 and the second equation by 10 to make the coefficients of k the same:

33 * (10 * k + 48 * f) = 33 * 161
10 * (33 * k - 41 * f) = 10 * 31

This gives us:

330 * k + 1584 * f = 5313
330 * k - 410 * f = 310

Now, we can subtract the second equation from the first to eliminate k:

(330 * k + 1584 * f) - (330 * k - 410 * f) = 5313 - 310

This simplifies to:

1994 * f = 4903

Now, we can solve for f:

f = 4903 / 1994

Now that we have the value of f, we can substitute it back into one of the original equations to find the value of k. Let's use the first equation:

10 * k + 48 * (4903 / 1994) = 161

This simplifies to:

10 * k + 235.4 = 161

Now, we can solve for k:

k = (161 - 235.4) / 10

k = -7.44

Therefore, the values of k and f that satisfy the system of equations are k = -7.44 and f = 4903 / 1994.

### Answer: k = -7.44, f = 4903 / 1994

Expected answer: {f: 5003/1994, k: 8089/1994}

Correct? No

Problem: Solve the following system of equations for the values of l and n: The first equation is 31 = 58 * l - n The second equation is 103 = n + 73 * l

Mixtral 8x22B:

 Reasoning:

Let's solve the first equation for n:
n = 58 * l - 31

Now, let's substitute this expression for n into the second equation:
103 = (58 * l - 31) + 73 * l

Combine like terms:
103 = 131 * l - 31

Now, let's solve for l:
131 * l = 103 + 31
131 * l = 134

Divide both sides by 131:
l = 134 / 131

Now, let's substitute this value of l back into the expression for n:
n = 58 * (134 / 131) - 31

Simplify:
n = 58 * 1.0229 - 31
n = 59.3138 - 31
n = 28.3138

So, the values of l and n are:
l = 134 / 131
n = 28.3138

### Answer: l = 134/131, n = 28.3138

Expected answer: {l: 134/131, n: 3711/131}

Correct? No

Problem: Find the values of y and j that satisfy the following system of equations: 29y - 28j = 39 25y + 37j = 116

Mixtral 8x22B:

 Reasoning: To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 25 and the second equation by 29 to eliminate y:

25(29y - 28j) = 25(39)
29(25y + 37j) = 29(116)

This gives us:

725y - 700j = 975
725y + 1073j = 3364

Now, we can subtract the first equation from the second equation to eliminate y:

(725y + 1073j) - (725y - 700j) = 3364 - 975

This simplifies to:

1773j = 2389

Now, we can solve for j:

j = 2389 / 1773

To find the value of y, we can substitute the value of j back into one of the original equations. Let's use the first equation:

29y - 28(2389 / 1773) = 39

This simplifies to:

29y - 168 = 39

Now, we can solve for y:

29y = 39 + 168
29y = 207

y = 207 / 29

Therefore, the values of y and j that satisfy the system of equations are:

y = 7
j = 1.35

### Answer: y = 7, j = 1.35

Expected answer: {j: 2389/1773, y: 4691/1773}

Correct? No

Problem: Given the following system of equations, solve for u and a: The first equation is 93u - 85a = 74 The second equation is 96u + 17a = 186.

Mixtral 8x22B:

 Reasoning: To solve for u and a, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 17 and the second equation by 85 to eliminate the variable a:

17(93u - 85a) = 17(74)
85(96u + 17a) = 85(186)

This gives us:

1581u - 1445a = 1258
8064u + 1445a = 15810

Now, we can add the two equations to eliminate the variable a:

1581u + 8064u = 1258 + 15810
9645u = 17068

Now, we can solve for u:

u = 17068 / 9645

Now that we have the value of u, we can substitute it back into one of the original equations to solve for a. Let's use the first equation:

93u - 85a = 74

Substitute the value of u:

93(17068 / 9645) - 85a = 74

Now, we can solve for a:

a = (93(17068 / 9645) - 74) / 85

Now, we can calculate the values of u and a:

u = 17068 / 9645 = <<17068/9645=1.7692307692307692>>1.7692307692307692
a = (93(17068 / 9645) - 74) / 85 = <<(93*(17068/9645)-74)/85=1.6923076923076923>>1.6923076923076923

### Answer: u = 1.7692307692307692, a = 1.6923076923076923

Expected answer: {a: 3398/3247, u: 1004/573}

Correct? No

Problem: Given the following pair of simultaneous equations, please find out the values of u and g: 97 * u - 61 * g = 15 85 * u + 23 * g = 186

Mixtral 8x22B:

 Reasoning:

To solve for u and g, we can use the method of substitution or elimination. Here, we will use the elimination method.

First, we can multiply the first equation by 23 and the second equation by 61 to make the coefficients of g the same:

(97 * u - 61 * g) * 23 = 15 * 23
(85 * u + 23 * g) * 61 = 186 * 61

This gives us:

2231 * u - 1403 * g = 345
5185 * u + 1403 * g = 11346

Now, we can add these two equations to eliminate g:

2231 * u + 5185 * u = 345 + 11346
7416 * u = 11691

Now, we can solve for u:

u = 11691 / 7416

Now that we have the value of u, we can substitute it back into one of the original equations to find the value of g. Let's use the first equation:

97 * u - 61 * g = 15

Substituting the value of u:

97 * (11691 / 7416) - 61 * g = 15

Now, we can solve for g:

g = (97 * (11691 / 7416) - 15) / 61

After calculating the values of u and g, we get:

u = 1.577
g = 1.234

### Answer: u = 1.577, g = 1.234

Expected answer: {g: 1863/824, u: 1299/824}

Correct? No

Problem: Determine the values of r and b that satisfy the following system of equations. The first equation is (17 * r) + (67 * b) = 103. The second equation is (85 * r) + (67 * b) = 187.

Mixtral 8x22B:

 Reasoning: To solve this system of equations, we can use the method of substitution or elimination. In this case, we will use the method of elimination.

First, we can subtract the first equation from the second equation to eliminate the variable b:

(85r + 67b) - (17r + 67b) = 187 - 103

This simplifies to:

68r = 84

Now, we can solve for r:

r = 84 / 68

r = 1.2352941176470588

Next, we can substitute the value of r back into either of the original equations to solve for b. We will use the first equation:

(17 * 1.2352941176470588) + (67 * b) = 103

This simplifies to:

21.000000000000004 + 67b = 103

Now, we can solve for b:

67b = 103 - 21.000000000000004

67b = 81.99999999999999

b = 81.99999999999999 / 67

b = 1.2238805969202454

Therefore, the values of r and b that satisfy the given system of equations are r = 1.2352941176470588 and b = 1.2238805969202454.

### Answer: r = 1.2352941176470588, b = 1.2238805969202454

Expected answer: {b: 82/67, r: 21/17}

Correct? No

Problem: Given the following system of equations, solve for the values of t and n: 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for n:

n = (41 + 54t) / 85

Now, let's substitute this expression for n into the second equation:

38t + 30((41 + 54t) / 85) = 126

Multiplying both sides by 85 to eliminate the fraction:

3230t + 1230 + 1620t = 10620

Combining like terms:

4850t + 1230 = 10620

Subtracting 1230 from both sides:

4850t = 9390

Dividing both sides by 4850:

t = 9390 / 4850

t = 1.936082474226804

Now, let's substitute this value of t back into the expression for n:

n = (41 + 54(1.936082474226804)) / 85

n = (41 + 104.2286567164678) / 85

n = 145.2286567164678 / 85

n = 1.708572431958445

Therefore, the values of t and n are approximately 1.936 and 1.709, respectively.

### Answer: t ≈ 1.936, n ≈ 1.709

Expected answer: {n: 4181/2425, t: 948/485}

Correct? No

Problem: Solve the following system of equations for the values of u and q: 1) The result of multiplying 75 by u and subtracting the product of 69 and q is equal to 5. 2) The sum of the product of 48 and u and the product of 25 and q is 140.

Mixtral 8x22B:

 Reasoning:

1) The first equation can be written as: 75u - 69q = 5

2) The second equation can be written as: 48u + 25q = 140

To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 25 and the second equation by 69 to eliminate q:

25(75u - 69q) = 25(5)
69(48u + 25q) = 69(140)

This gives us:

1875u - 1725q = 125
3312u + 1725q = 10060

Now, we can add these two equations to eliminate q:

1875u + 3312u = 125 + 10060
5187u = 10185

Now, we can solve for u:

u = 10185 / 5187
u = 2

Now that we have the value of u, we can substitute it back into one of the original equations to find the value of q. Let's use the second equation:

48(2) + 25q = 140
96 + 25q = 140

Now, we can solve for q:

25q = 140 - 96
25q = 44

q = 44 / 25
q = 1.76

Therefore, the values of u and q are:

u = 2
q = 1.76

### Answer: u = 2, q = 1.76

Expected answer: {q: 180/91, u: 515/273}

Correct? No

Problem: Determine the values of v and x from the following system of equations: ((20 * v) + (17 * x)) = 149 and ((24 * x) - (49 * v)) = 22.

Mixtral 8x22B:

 Reasoning: We can solve this system of equations by using the method of substitution or elimination. Let's use the method of elimination.

First, we can multiply the first equation by 49 and the second equation by 20 to eliminate the variable v:

(49 * (20 * v) + 49 * (17 * x)) = 49 * 149
(20 * (24 * x) - 20 * (49 * v)) = 20 * 22

Now, we can simplify and combine the equations:

(980 * v) + (833 * x) = 7301
(480 * x) - (980 * v) = 440

Next, we can add the two equations to eliminate the variable v:

(833 * x) + (480 * x) = 7301 + 440
(1313 * x) = 7741

Now, we can solve for x:

x = 7741 / 1313
x = <<7741/1313=5.894>>5.894

Next, we can substitute the value of x back into one of the original equations to solve for v:

(20 * v) + (17 * 5.894) = 149
(20 * v) + 100.2 = 149

Now, we can solve for v:

v = (149 - 100.2) / 20
v = <<(149-100.2)/20=2.44>>2.44

Therefore, the values of v and x are v = 2.44 and x = 5.894.

### Answer: v = 2.44, x = 5.894

Expected answer: {v: 3202/1313, x: 7741/1313}

Correct? No

Problem: Solve the following system of equations for the values of t and g: 39 * t + 41 * g = 147 94 * t - 91 * g = 42.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's try the elimination method. We can multiply the first equation by 91 and the second equation by 41 to eliminate g:

(39 * t + 41 * g) * 91 = 147 * 91
(94 * t - 91 * g) * 41 = 42 * 41

Now, we have:

3549 * t + 3731 * g = 13377
3854 * t - 3731 * g = 1722

Adding these two equations, we get:

7403 * t = 15099

Now, we can solve for t:

t = 15099 / 7403 = <<15099/7403=2.039>>2.039

Now, let's substitute the value of t into the first equation to find the value of g:

39 * 2.039 + 41 * g = 147

Now, we have:

79.421 + 41 * g = 147

Subtracting 79.421 from both sides, we get:

41 * g = 67.579

Now, we can solve for g:

g = 67.579 / 41 = <<67.579/41=1.648>>1.648

Therefore, the values of t and g are t = 2.039 and g = 1.648.

### Answer: t = 2.039, g = 1.648

Expected answer: {g: 12180/7403, t: 15099/7403}

Correct? No

Problem: Determine the values of c and o that satisfy the following system of equations: 6c + 55o = 112, and 55c - 48o = 36.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 48 and the second equation by 55 to eliminate the variable o:

48(6c + 55o) = 48(112)
55(55c - 48o) = 55(36)

This gives us:

288c + 2640o = 5376
3025c - 2640o = 1980

Now, we can add these two equations to eliminate the variable o:

288c + 3025c = 5376 + 1980
5913c = 7356

Now, we can solve for c:

c = 7356 / 5913
c = <<7356/5913=1.2439>>1.2439

Now that we have the value of c, we can substitute it back into one of the original equations to solve for o:

6(1.2439) + 55o = 112
7.4634 + 55o = 112
55o = 112 - 7.4634
55o = 104.5366
o = 104.5366 / 55
o = <<104.5366/55=1.9007>>1.9007

Therefore, the values of c and o that satisfy the system of equations are c = 1.2439 and o = 1.9007.

### Answer: c = 1.2439, o = 1.9007

Expected answer: {c: 7356/3313, o: 5944/3313}

Correct? No

Problem: Determine the values of u and w that satisfy the following system of equations: 8w + 68u = 170, 71w - 94u = 8.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for w:

8w + 68u = 170

Divide both sides by 8:

w + 8.5u = 21.25

Now, let's solve the second equation for w:

71w - 94u = 8

Divide both sides by 71:

w - 1.324u = 0.1127

Now, we have two equations with w:

w + 8.5u = 21.25
w - 1.324u = 0.1127

Subtract the second equation from the first:

9.824u = 21.1373

Divide both sides by 9.824:

u = 2.15

Now, substitute u = 2.15 into the first equation:

w + 8.5(2.15) = 21.25

w + 18.175 = 21.25

Subtract 18.175 from both sides:

w = 3.075

So, the values of u and w that satisfy the system of equations are u = 2.15 and w = 3.075.

### Answer: u = 2.15, w = 3.075

Expected answer: {u: 667/310, w: 459/155}

Correct? No

Problem: Solve the following system of equations for the values of r and f: 68*r + 8*f = 92 97*f + 38*r = 182

Mixtral 8x22B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Here, I will use the elimination method.

First, we can multiply the first equation by 38 and the second equation by 68 to make the coefficients of r equal:

(68*r + 8*f)*38 = 92*38
(97*f + 38*r)*68 = 182*68

This gives us:

2584*r + 304*f = 3516
6596*f + 2584*r = 12376

Now, we can subtract the first equation from the second equation to eliminate r:

6596*f + 2584*r - (2584*r + 304*f) = 12376 - 3516
6596*f - 304*f = 12376 - 3516
6292*f = 8860

Now, we can solve for f:

f = 8860 / 6292
f = <<8860/6292=1.4081>>1.4081

Now that we have the value of f, we can substitute it back into one of the original equations to solve for r:

68*r + 8*1.4081 = 92
68*r + 11.2648 = 92
68*r = 92 - 11.2648
68*r = 80.7352

Now, we can solve for r:

r = 80.7352 / 68
r = <<80.7352/68=1.1873>>1.1873

Therefore, the values of r and f are:

r = 1.1873
f = 1.4081

### Answer: r = 1.1873, f = 1.4081

Expected answer: {f: 2220/1573, r: 1867/1573}

Correct? No

Problem: Given the equations below, find the values of r and d: For the first equation, consider 67 apples, each worth d dollars, and 37 ragdolls, each worth r dollars. If the total value of all these items is $50, you can represent this situation with the equation 67d - 37r = 50. In another case, consider 39 ragdolls, each worth r dollars, and 21 apples, each worth d dollars. If the total value of all these items is $16, you can also represent this situation with the equation 39r - 21d = 16. From these two equations, find the values of d (the cost of each apple) and r (the cost of each ragdoll).

Mixtral 8x22B:

 Reasoning: We have two equations with two variables:

1) 67d - 37r = 50
2) 39r - 21d = 16

We can solve this system of equations using substitution or elimination. Let's use the elimination method.

First, we can multiply equation 1 by 21 and equation 2 by 37 to make the coefficients of d equal:

1) 21 * (67d - 37r) = 21 * 50
2) 37 * (39r - 21d) = 37 * 16

This gives us:

1) 1407d - 777r = 1050
2) 1443r - 777d = 592

Now, we can add these two equations to eliminate d:

1407d - 777r + 1443r - 777d = 1050 + 592

This simplifies to:

666r = 1642

Now, we can solve for r:

r = 1642 / 666
r = 2.4654654654654654

Now that we have the value of r, we can substitute it back into one of the original equations to find the value of d. Let's use equation 1:

67d - 37 * 2.4654654654654654 = 50

This simplifies to:

67d - 91.2 = 50

Now, we can solve for d:

67d = 141.2
d = 141.2 / 67
d = 2.107462686567164

Therefore, the cost of each apple is approximately $2.11 and the cost of each ragdoll is approximately $2.47.

### Answer: d ≈ $2.11, r ≈ $2.47

Expected answer: {d: 1271/918, r: 1061/918}

Correct? No

Problem: To find the values of x and a, solve the following system of simultaneous linear equations: First equation: 163 equals 50 times x plus a Second equation: 24 equals 98 times x minus 84 times a.

Mixtral 8x22B:

 Reasoning:
First, let's rewrite the equations in standard form:

1) 50x + a = 163
2) 98x - 84a = 24

Now, let's solve the first equation for a:

a = 163 - 50x

Next, substitute this expression for a into the second equation:

98x - 84(163 - 50x) = 24

Simplify the equation:

98x - 13644 + 4200x = 24

Combine like terms:

5198x = 13668

Now, divide both sides by 5198 to find the value of x:

x = 13668 / 5198

x = 2.63

Now, substitute the value of x back into the expression for a:

a = 163 - 50(2.63)

a = 163 - 131.5

a = 31.5

So, the values of x and a are:

x = 2.63
a = 31.5

### Answer: x = 2.63, a = 31.5

Expected answer: {a: 7387/2149, x: 6858/2149}

Correct? No

Problem: Solve the following system of equations for the values of p and b: 67 * p + 18 * b = 110 82 * b - 44 * p = 58.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for p:

67p + 18b = 110
67p = 110 - 18b
p = (110 - 18b) / 67

Now, let's substitute this expression for p into the second equation:

82b - 44((110 - 18b) / 67) = 58
82b - (44 * 110 / 67) + (44 * 18b / 67) = 58
82b - (44 * 110 / 67) + (44 * 18 / 67)b = 58

Now, let's simplify the equation:

82b - (44 * 110 / 67) + (44 * 18 / 67)b = 58
(82 + (44 * 18 / 67))b - (44 * 110 / 67) = 58
(82 + (44 * 18 / 67))b = 58 + (44 * 110 / 67)

Now, let's solve for b:

b = (58 + (44 * 110 / 67)) / (82 + (44 * 18 / 67))

Now, let's substitute this expression for b into the first equation to find the value of p:

p = (110 - 18b) / 67
p = (110 - 18((58 + (44 * 110 / 67)) / (82 + (44 * 18 / 67)))) / 67

Now, let's simplify the equation:

p = (110 - (18 * 58 / (82 + (44 * 18 / 67))) - (18 * (44 * 110 / 67) / (82 + (44 * 18 / 67)))) / 67

Now, let's calculate the values of p and b:

p = (110 - (18 * 58 / (82 + (44 * 18 / 67))) - (18 * (44 * 110 / 67) / (82 + (44 * 18 / 67)))) / 67
p = (110 - (18 * 58 / 82.42) - (18 * 74.63 / 82.42)) / 67
p = (110 - 10.42 - 13.42) / 67
p = 86.16 / 67
p = 1.286

b = (58 + (44 * 110 / 67)) / (82 + (44 * 18 / 67))
b = (58 + 74.63) / 82.42
b = 132.63 / 82.42
b = 1.61

Therefore, the values of p and b are p = 1.286 and b = 1.61.

### Answer: p = 1.286, b = 1.61

Expected answer: {b: 4363/3143, p: 3988/3143}

Correct? No

Problem: Determine the values of c and e from the following simultaneous equations: The difference between 63 times c and 36 times e equals 27, and 8 times c added to 32 times e equals 69.

Mixtral 8x22B:

 Reasoning: The first equation is 63c - 36e = 27.
The second equation is 8c + 32e = 69.

We can solve this system of equations by using the method of substitution or elimination. Let's use the method of elimination.

First, we can multiply the second equation by 3 to make the coefficients of e the same in both equations:

3(8c + 32e) = 3(69)
24c + 96e = 207

Now, we can subtract the first equation from this new equation to eliminate e:

(24c + 96e) - (63c - 36e) = 207 - 27
24c + 96e - 63c + 36e = 180
-39c + 132e = 180

Now, we can solve for c by dividing both sides by -39:

c = 180 / -39
c = -4.615384615384615

Next, we can substitute this value of c into either of the original equations to solve for e. Let's use the first equation:

63(-4.615384615384615) - 36e = 27
-290.00000000000006 - 36e = 27
-36e = 27 + 290.00000000000006
-36e = 317.00000000000006

Now, we can solve for e by dividing both sides by -36:

e = 317.00000000000006 / -36
e = -8.805555555555556

Therefore, the values of c and e are:

c = -4.615384615384615
e = -8.805555555555556

### Answer: c = -4.615384615384615, e = -8.805555555555556

Expected answer: {c: 93/64, e: 459/256}

Correct? No

Problem: Solve the following system of linear equations to find the values of x and p: 26 * x + 29 * p = 107 61 * x - 51 * p = 4

Mixtral 8x22B:

 Reasoning:

First, we can multiply the second equation by 29 and the first equation by 51 to eliminate p.

(26 * x + 29 * p) * 51 = 107 * 51
(61 * x - 51 * p) * 29 = 4 * 29

This gives us:

1326 * x + 1479 * p = 5457
1769 * x - 1479 * p = 116

Adding these two equations together, we get:

1326 * x + 1769 * x = 5457 + 116
3095 * x = 5573

Dividing both sides by 3095, we get:

x = 5573 / 3095

Now, we can substitute this value of x back into one of the original equations to find the value of p.

26 * (5573 / 3095) + 29 * p = 107

Multiplying both sides by 3095, we get:

1769 * 5573 + 29 * 3095 * p = 107 * 3095

This simplifies to:

9854477 + 89755 * p = 330485

Subtracting 9854477 from both sides, we get:

89755 * p = -9523622

Dividing both sides by 89755, we get:

p = -9523622 / 89755

Therefore, the values of x and p are:

x = 5573 / 3095
p = -9523622 / 89755

### Answer: x = 1.8, p = -106.1

Expected answer: {p: 6423/3095, x: 5573/3095}

Correct? No

Problem: Find the values for g and l from the system of equations below. The first equation is: ((29 * l) + (17 * g)) = 68. The second equation is: ((31 * g) - (10 * l)) = 17.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

Using the elimination method, we can multiply the first equation by 10 and the second equation by 17 to eliminate l:

10 * ((29 * l) + (17 * g)) = 10 * 68
17 * ((31 * g) - (10 * l)) = 17 * 17

This gives us:

290l + 170g = 680
527g - 170l = 289

Now, we can add these two equations to eliminate l:

290l + 170g + 527g - 170l = 680 + 289
797g = 969

Now, we can solve for g:

g = 969 / 797

Now that we have the value for g, we can substitute it back into one of the original equations to find the value for l. Let's use the first equation:

(29 * l) + (17 * (969 / 797)) = 68

Now, we can solve for l:

29l + (17 * 1.215) = 68
29l + 20.655 = 68
29l = 47.345

Now, we can solve for l:

l = 47.345 / 29

So, the values for g and l are:

g = 1.215
l = 1.632

### Answer: g = 1.215, l = 1.632

Expected answer: {g: 1173/1069, l: 1819/1069}

Correct? No

Problem: Given the following system of equations, what are the values for a and c? 33*a - 54*c = 20 24*a - 26*c = 29.

Mixtral 8x22B:

 Reasoning:

We can solve this system of equations using the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the second equation by 2 to make the coefficients of a in both equations the same:

2 * (24a - 26c) = 2 * 29
48a - 52c = 58

Now, we can subtract the first equation from this new equation to eliminate a:

(48a - 52c) - (33a - 54c) = 58 - 20
15a + 2c = 38

Next, we can multiply this new equation by 3 to make the coefficients of c in both equations the same:

3 * (15a + 2c) = 3 * 38
45a + 6c = 114

Now, we can subtract the first equation from this new equation to eliminate c:

(45a + 6c) - (33a - 54c) = 114 - 20
12a + 60c = 94

Now, we can solve for a by dividing both sides of the equation by 12:

a = 94 / 12
a = 7.8333

Next, we can substitute this value of a back into one of the original equations to solve for c:

33 * 7.8333 - 54c = 20
258.3333 - 54c = 20
54c = 238.3333
c = 238.3333 / 54
c = 4.4135

Therefore, the values for a and c are approximately 7.8333 and 4.4135, respectively.

### Answer: a ≈ 7.8333, c ≈ 4.4135

Expected answer: {a: 523/219, c: 159/146}

Correct? No

Problem: Kat found herself stuck solving the following system of equations with two variables, d and j. Can you help her resolve it? 71d + 9j = 132 43j - 84d = 91.

Mixtral 8x22B:

 Reasoning: To solve this system of equations, we can use the method of substitution or elimination. Here, I will use the elimination method.

First, we can multiply the first equation by 84 and the second equation by 71 to make the coefficients of d in both equations equal:

(71d + 9j) * 84 = 132 * 84
(43j - 84d) * 71 = 91 * 71

This gives us:

5964d + 7056j = 11088
-5964d + 3053j = 6461

Now, we can add these two equations to eliminate d:

7056j + 3053j = 11088 + 6461
10109j = 17549

Now, we can solve for j:

j = 17549 / 10109
j = <<17549/10109=1.736>>1.736 (approximately)

Next, we can substitute the value of j back into one of the original equations to solve for d. Let's use the first equation:

71d + 9(1.736) = 132
71d + 15.624 = 132

Now, we can solve for d:

71d = 132 - 15.624
71d = 116.376

d = 116.376 / 71
d = <<116.376/71=1.639>>1.639 (approximately)

Therefore, the solution to the system of equations is approximately d = 1.639 and j = 1.736.

### Answer: d = 1.639, j = 1.736 (approximately)

Expected answer: {d: 4857/3809, j: 17549/3809}

Correct? No

Problem: Determine the values of o and n by solving this system of equations: (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143.

Mixtral 8x22B:

 Reasoning:

Let's solve this system of equations using the substitution or elimination method.

First, let's rewrite the equations:

1. 81o + 26n = 163
2. 87n + 23o = 143

We can multiply the first equation by 23 and the second equation by 26 to eliminate one of the variables:

1. 23(81o + 26n) = 23(163)
2. 26(87n + 23o) = 26(143)

This gives us:

1. 1863o + 609n = 3749
2. 2262n + 609o = 3718

Now, let's subtract the second equation from the first to eliminate o:

1863o - 609o + 609n - 2262n = 3749 - 3718

This simplifies to:

1254o - 1653n = 31

Now, let's solve for o:

o = (31 + 1653n) / 1254

Now, let's substitute this expression for o into the first original equation:

81((31 + 1653n) / 1254) + 26n = 163

This simplifies to:

2511 + 134253n + 31226n = 201426

Now, let's solve for n:

n = (201426 - 2511) / 165479

n = 198915 / 165479

n = 1.2

Now, let's substitute n = 1.2 into the expression for o:

o = (31 + 1653(1.2)) / 1254

o = (31 + 1983.6) / 1254

o = 2014.6 / 1254

o = 1.6

Therefore, the values of o and n are:

o = 1.6
n = 1.2

### Answer: o = 1.6, n = 1.2

Expected answer: {n: 7834/6449, o: 10463/6449}

Correct? No

Problem: Solve the following system of equations for w and s: 46 * s - 61 * w = 2 61 * s + 67 * w = 178.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

Using the elimination method, we can multiply the first equation by 61 and the second equation by 46 to eliminate the variable s:

(46 \* 61)s - (61 \* 61)w = 2 \* 61
(61 \* 46)s + (67 \* 46)w = 178 \* 46

Now, we can subtract the first equation from the second equation to eliminate s:

(67 \* 46)w - (-61 \* 61)w = 178 \* 46 - 2 \* 61

Now, we can solve for w:

w = (178 \* 46 - 2 \* 61) / (67 \* 46 + 61 \* 61)

Now, we can substitute the value of w back into one of the original equations to solve for s.

Let's substitute w into the first equation:

46s - 61w = 2

Now, we can solve for s:

s = (2 + 61w) / 46

Now, we can substitute the value of w back into the equation for s to find the value of s.

### Answer: w = <<(178 \* 46 - 2 \* 61) / (67 \* 46 + 61 \* 61)=0.5>>0.5, s = <<(2 + 61 \* 0.5) / 46=1.5>>1.5

Expected answer: {s: 10992/6803, w: 8066/6803}

Correct? No

Problem: In the following system of equations, calculate the values of i and k. System of equations: 51*k - 8*i = 86 39*i + 8*k = 193.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for k:

51k - 8i = 86
51k = 86 + 8i
k = (86 + 8i) / 51

Now, let's substitute this expression for k into the second equation:

39i + 8((86 + 8i) / 51) = 193

Now, let's solve for i:

39i + (688 + 64i) / 51 = 193
(39i * 51) + (688 + 64i) = 193 * 51
1989i + 688 + 64i = 9843
2053i = 9843 - 688
2053i = 9155
i = 9155 / 2053
i = 4.46 (approximately)

Now, let's substitute the value of i back into the expression for k:

k = (86 + 8(4.46)) / 51
k = (86 + 35.68) / 51
k = 121.68 / 51
k = 2.39 (approximately)

So, the values of i and k are approximately 4.46 and 2.39, respectively.

### Answer: i ≈ 4.46, k ≈ 2.39

Expected answer: {i: 9155/2053, k: 4898/2053}

Correct? No

Problem: Solve the following system of equations for the values of l and m: 26m + 17l = 146 93m + l = 126

Mixtral 8x22B:

 Reasoning:

First, we can solve for l in the second equation:

l = 126 - 93m

Now, we can substitute this expression for l into the first equation:

26m + 17(126 - 93m) = 146

Expanding the equation, we get:

26m + 2142 - 1581m = 146

Combining like terms, we get:

-1555m + 2142 = 146

Subtracting 2142 from both sides, we get:

-1555m = -1996

Dividing both sides by -1555, we get:

m = 1.28

Now, we can substitute this value of m back into the equation for l:

l = 126 - 93(1.28)

l = 126 - 119.04

l = 6.96

Therefore, the solution to the system of equations is:

m = 1.28
l = 6.96

### Answer: m = 1.28, l = 6.96

Expected answer: {l: 10302/1555, m: 1996/1555}

Correct? No

Problem: Determine the values of 'h' and 'f' by solving the following system of equations: 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119

Mixtral 8x22B:

 Reasoning:

To solve the system of equations, we can use the method of substitution or elimination. In this case, we will use the method of elimination.

First, we can multiply equation 1 by 46 and equation 2 by 39 to make the coefficients of 'h' the same:

1) (46 \* 8 \* f) + (46 \* 39 \* h) = 46 \* 66

2) (39 \* 29 \* f) + (39 \* 46 \* h) = 39 \* 119

Now, we can subtract equation 2 from equation 1 to eliminate 'h':

(46 \* 8 \* f) - (39 \* 29 \* f) = 46 \* 66 - 39 \* 119

Simplifying the equation, we get:

(368 \* f) - (1131 \* f) = 3018 - 4641

-763 \* f = -1623

Now, we can solve for 'f':

f = -1623 / -763

f = 2.128

Now that we have the value of 'f', we can substitute it back into either equation 1 or 2 to solve for 'h'. Let's use equation 1:

(8 \* 2.128) + (39 \* h) = 66

17.024 + 39 \* h = 66

Now, we can solve for 'h':

39 \* h = 66 - 17.024

39 \* h = 48.976

h = 48.976 / 39

h = 1.256

Therefore, the values of 'h' and 'f' are:

h = 1.256

f = 2.128

### Answer: h = 1.256, f = 2.128

Expected answer: {f: 1605/763, h: 962/763}

Correct? No

Problem: Find the values of k and b that satisfy the following system of equations: 22 * b + 23 * k = 109 and 62 * k - 69 * b = 14.

Mixtral 8x22B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use elimination.

First, we can multiply the first equation by 69 and the second equation by 22 to eliminate b:

(22 * 69) * b + (23 * 69) * k = 109 * 69
(62 * 22) * k - (69 * 22) * b = 14 * 22

Now, we can add the two equations to eliminate b:

(22 * 69 + 62 * 22) * k = 109 * 69 + 14 * 22

Solving for k, we get:

k = (109 * 69 + 14 * 22) / (22 * 69 + 62 * 22)

Now, we can substitute the value of k back into one of the original equations to find the value of b. Let's use the first equation:

22 * b + 23 * k = 109

Substituting the value of k, we get:

22 * b + 23 * ((109 * 69 + 14 * 22) / (22 * 69 + 62 * 22)) = 109

Solving for b, we get:

b = (109 - 23 * ((109 * 69 + 14 * 22) / (22 * 69 + 62 * 22))) / 22

Therefore, the values of k and b that satisfy the system of equations are:

k = (109 * 69 + 14 * 22) / (22 * 69 + 62 * 22)
b = (109 - 23 * ((109 * 69 + 14 * 22) / (22 * 69 + 62 * 22))) / 22

### Answer: k = (109 * 69 + 14 * 22) / (22 * 69 + 62 * 22), b = (109 - 23 * ((109 * 69 + 14 * 22) / (22 * 69 + 62 * 22))) / 22

Expected answer: {b: 6436/2951, k: 7829/2951}

Correct? No

Problem: Solve the following system of linear equations for the values of m and s: 1. 84m - 55s = 1 2. 63m - 2s = 98.

Mixtral 8x22B:

 Reasoning:

First, we can solve the second equation for m:

63m = 98 + 2s
m = (98 + 2s) / 63

Now, we can substitute this expression for m into the first equation:

84((98 + 2s) / 63) - 55s = 1

Simplify the equation:

(84 * 98) / 63 + (168s) / 63 - 55s = 1

Multiply both sides by 63 to eliminate the fraction:

84 * 98 + 168s - 3465s = 63

Combine like terms:

84 * 98 - 3297s = 63

Now, we can solve for s:

3297s = 84 * 98 - 63
s = (84 * 98 - 63) / 3297

Now, we can substitute this value of s back into the expression for m:

m = (98 + 2((84 * 98 - 63) / 3297)) / 63

Simplify the expression for m:

m = (98 + (168 * 98 - 126) / 3297) / 63

Now, we can calculate the values of m and s:

s = (84 * 98 - 63) / 3297
m = (98 + (168 * 98 - 126) / 3297) / 63

### Answer: m = <<(98 + (168 * 98 - 126) / 3297) / 63>>, s = <<(84 * 98 - 63) / 3297>>

Expected answer: {m: 1796/1099, s: 389/157}

Correct? No

Problem: Given the following system of equations, find the values of b and k: 1. (6 * b) + (5 * k) = 105 2. (95 * k) - (51 * b) = 67.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method. I'll use the elimination method.

First, we can multiply the first equation by 51 and the second equation by 6 to make the coefficients of b equal:

(6 * 51 * b) + (5 * 51 * k) = 105 * 51
(95 * 6 * k) - (51 * 6 * b) = 67 * 6

Now, we can subtract the second equation from the first to eliminate b:

(6 * 51 * b) + (5 * 51 * k) - (95 * 6 * k) + (51 * 6 * b) = 105 * 51 - 67 * 6

Simplifying, we get:

(5 * 51 * k) - (95 * 6 * k) = 105 * 51 - 67 * 6

Now, we can factor out k:

k * (5 * 51 - 95 * 6) = 105 * 51 - 67 * 6

Simplifying further, we get:

k * (255 - 570) = 5355 - 402

k * (-315) = 4953

Now, we can solve for k:

k = 4953 / -315

k = -15.72

Now that we have the value of k, we can substitute it back into one of the original equations to find the value of b. Let's use the first equation:

(6 * b) + (5 * -15.72) = 105

Simplifying, we get:

6 * b - 78.6 = 105

Now, we can solve for b:

6 * b = 105 + 78.6

6 * b = 183.6

b = 183.6 / 6

b = 30.6

Therefore, the values of b and k are:

b = 30.6
k = -15.72

### Answer: b = 30.6, k = -15.72

Expected answer: {b: 1928/165, k: 1919/275}

Correct? No

Problem: Determine the values of d and u from the following pair of simultaneous linear equations: 33d + 62u = 114 and 32u + 40d = 83.

Mixtral 8x22B:

 Reasoning: To solve for d and u, we can use the method of substitution or elimination. Here, we will use the elimination method.

First, we can multiply the first equation by 40 and the second equation by 33 to make the coefficients of d equal:

(33d + 62u) \* 40 = 114 \* 40
(32u + 40d) \* 33 = 83 \* 33

This gives us:

1320d + 2480u = 4560
1056u + 1320d = 2739

Now, we can subtract the second equation from the first to eliminate d:

(1320d + 2480u) - (1056u + 1320d) = 4560 - 2739

This simplifies to:

1424u = 1821

Now, we can solve for u:

u = 1821 / 1424

Next, we can substitute the value of u back into one of the original equations to solve for d. Let's use the first equation:

33d + 62(1821 / 1424) = 114

This simplifies to:

33d + 80.99 = 114

Now, we can solve for d:

d = (114 - 80.99) / 33

Therefore, the values of d and u are:

d = <<(114 - 80.99) / 33=1.03>>1.03
u = <<1821 / 1424=1.2785714285714286>>1.2785714285714286

### Answer: d = 1.03, u = 1.2785714285714286

Expected answer: {d: 749/712, u: 1821/1424}

Correct? No

Problem: There are two equations below that contain the variables c and p. Can you solve this system of equations to find the values of c and p? 5 * c + 28 * p = 102 20 * c - 67 * p = 13

Mixtral 8x22B:

 Reasoning: To solve this system of equations, we can use the method of substitution or elimination. Here, I will use the method of elimination.

First, we can multiply the first equation by 4 to make the coefficients of c the same:

20 * c + 112 * p = 408

Now, we can subtract the second equation from this new equation to eliminate c:

(20 * c + 112 * p) - (20 * c - 67 * p) = 408 - 13

This simplifies to:

179 * p = 395

Now, we can solve for p:

p = 395 / 179

Now that we have the value of p, we can substitute it back into one of the original equations to find the value of c. Let's use the first equation:

5 * c + 28 * (395 / 179) = 102

This simplifies to:

5 * c + 28 * 2.2067 = 102

Now, we can solve for c:

c = (102 - 28 * 2.2067) / 5

c = (102 - 61.7876) / 5

c = 40.2124 / 5

c = 8.04248

So, the values of c and p are:

c = 8.04248
p = 2.2067

### Answer: c = 8.04248, p = 2.2067

Expected answer: {c: 7198/895, p: 395/179}

Correct? No

Problem: Given the following system of linear equations, determine the value of r and q. The system of equations is: 58 * r + 12 * q = 147 97 * q - 76 * r = 76.

Mixtral 8x22B:

 Reasoning: To solve the system of linear equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 76 and the second equation by 58 to eliminate r:

(58 * r + 12 * q) * 76 = 147 * 76
(97 * q - 76 * r) * 58 = 76 * 58

This gives us:

4408 * r + 912 * q = 11172
5626 * q - 4408 * r = 4408

Now, we can add the two equations to eliminate r:

4408 * r + 912 * q + 5626 * q - 4408 * r = 11172 + 4408

This simplifies to:

6538 * q = 15580

Now, we can solve for q:

q = 15580 / 6538

Now, we can substitute the value of q back into one of the original equations to solve for r. Let's use the first equation:

58 * r + 12 * (15580 / 6538) = 147

This simplifies to:

58 * r + 294.24 = 147

Now, we can solve for r:

r = (147 - 294.24) / 58

Now, we can calculate the values of r and q:

q = 15580 / 6538 = <<15580/6538=2.383>>2.383 (rounded to three decimal places)
r = (147 - 294.24) / 58 = <<(147-294.24)/58=-2.46>>-2.46 (rounded to two decimal places)

### Answer: r = -2.46, q = 2.383

Expected answer: {q: 7790/3269, r: 13347/6538}

Correct? No

Problem: Resolve the provided system of simultaneous linear equations for v and k: 47 * v - 3 * k = 10 73 * v + 2 * k = 128.

Mixtral 8x22B:

 Reasoning:

First, we can multiply the first equation by 2 and the second equation by 3 to eliminate k:

2 * (47 * v - 3 * k) = 2 * 10
3 * (73 * v + 2 * k) = 3 * 128

This gives us:

94 * v - 6 * k = 20
219 * v + 6 * k = 384

Adding these two equations together, we get:

313 * v = 404

Now, we can solve for v:

v = 404 / 313 = <<404/313=1.2907348236421724>>1.2907348236421724

Next, we can substitute this value of v into one of the original equations to solve for k. Let's use the first equation:

47 * 1.2907348236421724 - 3 * k = 10

Now, we can solve for k:

k = (47 * 1.2907348236421724 - 10) / 3 = <<(47 * 1.2907348236421724 - 10) / 3=11.290734823642172>>11.290734823642172

Therefore, the solution to the system of equations is:

v = 1.2907348236421724
k = 11.290734823642172

### Answer: v = 1.2907348236421724, k = 11.290734823642172

Expected answer: {k: 5286/313, v: 404/313}

Correct? No

Problem: You are given the following system of equations: The result of 89 multiplied by p minus 41 multiplied by q equals 60. The result of 27 multiplied by p plus 91 multiplied by q equals 124. What are the values of p and q?

Mixtral 8x22B:

 Reasoning: Let's write the system of equations as follows:
89p - 41q = 60
27p + 91q = 124

We can solve this system using the method of substitution or elimination. Let's use the method of elimination.

First, we can multiply the first equation by 27 and the second equation by 89 to eliminate q:

27(89p - 41q) = 27(60)
89(27p + 91q) = 89(124)

This gives us:
2403p - 1107q = 1620
2403p + 8119q = 11074

Now, we can subtract the first equation from the second equation to eliminate p:

(2403p + 8119q) - (2403p - 1107q) = 11074 - 1620
8119q + 1107q = 9454

This simplifies to:
9226q = 9454

Now, we can solve for q:
q = 9454 / 9226
q = 1

Now that we have the value of q, we can substitute it back into one of the original equations to find the value of p. Let's use the first equation:

89p - 41(1) = 60
89p - 41 = 60
89p = 101

Now, we can solve for p:
p = 101 / 89
p = 1.1348314606741573

Therefore, the values of p and q are:
p = 1.1348314606741573
q = 1

### Answer: p = 1.1348314606741573, q = 1

Expected answer: {p: 5272/4603, q: 4708/4603}

Correct? No

Problem: Find the values of u and d that make these equations true: The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71

Mixtral 8x22B:

 To find the values of u and d that make these equations true, we can solve the system of equations using substitution or elimination. Here, we'll use the elimination method.

First, let's multiply the first equation by 3 and the second equation by 4 to make the coefficients of u and d the same:

(88 * u) - (96 * d) = 12
(27 * u) + (36 * d) = 71

Multiplying the first equation by 3:
(264 * u) - (288 * d) = 36

Multiplying the second equation by 4:
(108 * u) + (144 * d) = 284

Now, let's add the two equations to eliminate d:

(264 * u) - (288 * d) = 36
(108 * u) + (144 * d) = 284
----------------------------
(372 * u) = 320

Now, we can solve for u:

u = 320 / 372
u = 8 / 9

Now that we have the value of u, we can substitute it back into one of the original equations to find the value of d. Let's use the first equation:

(88 * u) - (96 * d) = 12
(88 * 8/9) - (96 * d) = 12
(704/9) - (96 * d) = 12

Now, let's solve for d:

96 * d = (704/9) - 12
96 * d = (704 - 108) / 9
96 * d = 596 / 9

d = 596 / (9 * 96)
d = 596 / 864
d = 745 / 1080

So, the values of u and d that make these equations true are:

u = 8/9
d = 745/1080

### Answer: u = 8/9, d = 745/1080

Expected answer: {d: 1481/1440, u: 151/120}

Correct? No

Problem: Solve the following system of equations for the values of f and n: 20 * n - 18 * f = 9 and 3 * n - 2 * f = 70.

Mixtral 8x22B:

 Reasoning:

First, we can solve the second equation for n:

3n - 2f = 70
3n = 70 + 2f
n = (70 + 2f)/3

Now, we can substitute this expression for n into the first equation:

20 * ((70 + 2f)/3) - 18 * f = 9

Multiplying both sides by 3 to eliminate the fraction:

20 * (70 + 2f) - 54 * f = 27

Expanding the equation:

1400 + 40f - 54f = 27

Combining like terms:

-14f = 27 - 1400

-14f = -1373

Dividing both sides by -14:

f = -1373/-14

f = 98.07

Now, we can substitute the value of f back into the expression for n:

n = (70 + 2 * 98.07)/3

n = (70 + 196.14)/3

n = 266.14/3

n = 88.71

Therefore, the solution to the system of equations is f = 98.07 and n = 88.71.

### Answer: f = 98.07, n = 88.71

Expected answer: {f: 1373/14, n: 621/7}

Correct? No

Problem: Determine the values of j and l from the following system of equations: 7 * l + 97 * j = 133 22 * j + 37 * l = 76.

Mixtral 8x22B:

 Reasoning:

We can solve this system of equations using the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 37 and the second equation by 97 to make the coefficients of l equal:

37 * (7 * l + 97 * j) = 37 * 133
97 * (22 * j + 37 * l) = 97 * 76

This gives us:

259 * l + 3609 * j = 4921
2234 * j + 3589 * l = 7392

Now, let's subtract the first equation from the second equation to eliminate l:

(2234 * j + 3589 * l) - (259 * l + 3609 * j) = 7392 - 4921

This simplifies to:

1875 * j = 2471

Now, let's solve for j:

j = 2471 / 1875

Now that we have the value of j, we can substitute it back into one of the original equations to find the value of l. Let's use the first equation:

7 * l + 97 * (2471 / 1875) = 133

This simplifies to:

7 * l + 239.996 = 133

Now, let's solve for l:

l = (133 - 239.996) / 7

l = -106.996 / 7

l = -15.285

So, the values of j and l are:

j = 2471 / 1875
l = -106.996 / 7

### Answer: j = 2471/1875, l = -106.996/7

Expected answer: {j: 1463/1145, l: 1482/1145}

Correct? No

Problem: Determine the values of d and f from the following system of equations: 21d - 46f = 53 8d + 84f = 133.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

First, we can multiply the first equation by 2 to make the coefficients of d the same in both equations:

42d - 92f = 106

Now, we can add the two equations to eliminate d:

(42d - 92f) + (8d + 84f) = 106 + 133

50d - 8f = 239

Now, we can solve for d:

d = (239 + 8f) / 50

Next, we can substitute this expression for d into the first equation to solve for f:

21((239 + 8f) / 50) - 46f = 53

Now, we can solve for f:

f = -11

Finally, we can substitute this value of f back into the expression for d to find its value:

d = (239 + 8(-11)) / 50

d = 3

Therefore, the values of d and f are d = 3 and f = -11.

### Answer: d = 3, f = -11

Expected answer: {d: 5285/1066, f: 2369/2132}

Correct? No

Problem: Determine the values of u and w that satisfy the following system of equations: 74u + 11w = 116 66u - 68w = 21.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the second equation by 11 to make the coefficients of w in both equations the same:

11*(66u - 68w) = 11*21
726u - 748w = 231

Now, we can add the two equations to eliminate w:

(74u + 11w) + (726u - 748w) = 116 + 231
74u + 726u = 347
800u = 347
u = 347/800

Now that we have the value of u, we can substitute it back into one of the original equations to find the value of w. Let's use the first equation:

74*(347/800) + 11w = 116
256.78 + 11w = 116
11w = 116 - 256.78
11w = -140.78
w = -140.78/11
w = -12.8

Therefore, the values of u and w that satisfy the given system of equations are u = 347/800 and w = -12.8.

### Answer: u = 347/800, w = -12.8

Expected answer: {u: 8119/5758, w: 3051/2879}

Correct? No

Problem: Find the values of f and j that will satisfy the following system of equations: 76 * f - 42 * j = 96 47 * j + 34 * f = 136.

Mixtral 8x22B:

 Reasoning: To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 34 and the second equation by 42 to make the coefficients of f and j the same:

34 * (76 * f - 42 * j) = 34 * 96
42 * (47 * j + 34 * f) = 42 * 136

This gives us:

2584 * f - 1428 * j = 3264
2014 * j + 1428 * f = 5712

Now, we can add these two equations to eliminate f:

2584 * f + 2014 * j - 1428 * j - 1428 * f = 3264 + 5712
1156 * f + 586 * j = 9976

Next, we can multiply the first equation by 586 and the second equation by 1156 to make the coefficients of f and j the same:

586 * (2584 * f - 1428 * j) = 586 * 3264
1156 * (1156 * f + 586 * j) = 1156 * 9976

This gives us:

1514224 * f - 838008 * j = 1911840
1336336 * f + 676936 * j = 11527136

Now, we can add these two equations to eliminate j:

1514224 * f + 1336336 * f = 1911840 + 11527136
2850560 * f = 13438976

Finally, we can solve for f:

f = 13438976 / 2850560
f = 4.714285714285714

Now that we have the value of f, we can substitute it back into one of the original equations to find the value of j:

76 * 4.714285714285714 - 42 * j = 96
359.99999999999994 - 42 * j = 96
-42 * j = 96 - 359.99999999999994
-42 * j = -263.99999999999994
j = 263.99999999999994 / 42
j = 6.285714285714286

Therefore, the values of f and j that satisfy the given system of equations are f = 4.714285714285714 and j = 6.285714285714286.

### Answer: f = 4.714285714285714, j = 6.285714285714286

Expected answer: {f: 1278/625, j: 884/625}

Correct? No

Problem: Consider the following system of equations. Find the values of u and e: 68u + 32e = 174 63e - 69u = 1.

Mixtral 8x22B:

 To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

First, we can multiply the second equation by 32 and the first equation by 63 to make the coefficients of e equal:

32 \* (63e - 69u) = 32 \* 1
63 \* (68u + 32e) = 63 \* 174

This gives us:

1952e - 2208u = 32
4284u + 2016e = 10962

Now, we can add the two equations to eliminate e:

(1952e - 2208u) + (4284u + 2016e) = 32 + 10962

This simplifies to:

6240u = 11024

Now, we can solve for u:

u = 11024 / 6240

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 8:

u = (11024 / 8) / (6240 / 8)
u = 1378 / 780

Now, we can simplify this fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

u = (1378 / 2) / (780 / 2)
u = 689 / 390

Now that we have the value of u, we can substitute it back into one of the original equations to find the value of e. Let's use the first equation:

68u + 32e = 174

Substituting the value of u, we get:

68 \* (689 / 390) + 32e = 174

Now, we can solve for e:

32e = 174 - 68 \* (689 / 390)
32e = 174 - (68 \* 689) / 390
32e = 174 - 46892 / 390
32e = 174 - 120.236
32e = 53.764

Now, we can solve for e:

e = 53.764 / 32
e = 1.68

Therefore, the values of u and e are:

u = 689 / 390
e = 1.68

### Answer: u = 689 / 390, e = 1.68

Expected answer: {e: 6037/3246, u: 5465/3246}

Correct? No

Problem: Find the values of p and n that satisfy the following system of linear equations: 57p + 4n = 129 and 24p + 39n = 154.

Mixtral 8x22B:

 Reasoning: To solve the system of linear equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 39 and the second equation by 4 to make the coefficients of n equal:

(57p + 4n) \* 39 = 129 \* 39
(24p + 39n) \* 4 = 154 \* 4

This gives us:

2223p + 152n = 5031
96p + 156n = 616

Now, we can subtract the second equation from the first to eliminate n:

2223p + 152n - (96p + 156n) = 5031 - 616
2223p - 96p + 152n - 156n = 4415
2127p - 4n = 4415

Now, we can solve for p:

2127p = 4415 + 4n
p = (4415 + 4n) / 2127

Next, we can substitute this expression for p back into one of the original equations to solve for n. Let's use the first equation:

57p + 4n = 129
57 \* ((4415 + 4n) / 2127) + 4n = 129

Now, we can solve for n:

(57 \* 4415 + 57 \* 4n) / 2127 + 4n = 129
(251405 + 228n) / 2127 + 4n = 129
251405 + 228n + 8508n = 129 \* 2127
251405 + 8736n = 274983
8736n = 274983 - 251405
8736n = 23578
n = 23578 / 8736
n = 2.7

Now that we have the value of n, we can substitute it back into the expression for p to find its value:

p = (4415 + 4 \* 2.7) / 2127
p = (4415 + 10.8) / 2127
p = 4425.8 / 2127
p = 2.08

Therefore, the values of p and n that satisfy the given system of linear equations are p = 2.08 and n = 2.7.

### Answer: p = 2.08, n = 2.7

Expected answer: {n: 1894/709, p: 4415/2127}

Correct? No

Problem: Determine the values of y and z from the given system of equations: 66 * z - 44 * y = 32 60 * y + 14 * z = 116.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

Using the elimination method, we can multiply the first equation by 14 and the second equation by 44 to eliminate y:

14 * (66 * z - 44 * y) = 14 * 32
44 * (60 * y + 14 * z) = 44 * 116

This gives us:

924 * z - 616 * y = 448
2640 * y + 616 * z = 5104

Now, we can add the two equations to eliminate y:

924 * z + 2640 * y - 616 * y + 616 * z = 448 + 5104

This simplifies to:

1540 * z = 5552

Now, we can solve for z:

z = 5552 / 1540
z = <<5552/1540=3.6>>3.6

Now that we have the value of z, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:

66 * 3.6 - 44 * y = 32

This simplifies to:

237.6 - 44 * y = 32

Now, we can solve for y:

44 * y = 237.6 - 32
44 * y = 205.6

y = 205.6 / 44
y = <<205.6/44=4.672727272727273>>4.672727272727273

Therefore, the values of y and z are approximately 4.67 and 3.6, respectively.

### Answer: y ≈ 4.67, z ≈ 3.6

Expected answer: {y: 901/572, z: 439/286}

Correct? No

Problem: Solve the following system of equations for the variables t and h: The first equation is 83 * t - 58 * h = 45. The second equation is 69 * h + 11 * t = 124.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the substitution or elimination method. Here, we will use the elimination method.

First, we can multiply the first equation by 11 and the second equation by 83 to eliminate the variable t:

83 * 11 * t - 58 * 11 * h = 45 * 11
69 * 83 * h + 11 * 83 * t = 124 * 83

This gives us:

913 * t - 638 * h = 495
5727 * h + 913 * t = 10292

Now, we can add the two equations to eliminate the variable t:

913 * t - 638 * h + 5727 * h + 913 * t = 495 + 10292

This simplifies to:

1826 * t + 5089 * h = 10787

Now, we can solve for the variable h:

h = (10787 - 1826 * t) / 5089

Next, we can substitute this expression for h back into one of the original equations to solve for t. Let's use the first equation:

83 * t - 58 * ((10787 - 1826 * t) / 5089) = 45

This simplifies to:

83 * t - 58 * (10787 / 5089) + 58 * (1826 / 5089) * t = 45

Now, we can solve for t:

t = (45 + 58 * (10787 / 5089)) / (83 + 58 * (1826 / 5089))

This gives us:

t = 1

Now that we have the value of t, we can substitute it back into the expression for h to find its value:

h = (10787 - 1826 * 1) / 5089

This simplifies to:

h = 1

Therefore, the solution to the system of equations is t = 1 and h = 1.

### Answer: t = 1, h = 1

Expected answer: {h: 9797/6365, t: 10297/6365}

Correct? No

Problem: Given the system of equations ((79 * h) - (61 * o)) = 9 and ((16 * h) - (12 * o)) = 9, what are the values of o and h?

Mixtral 8x22B:

 Reasoning:

First, let's simplify the system of equations by dividing the second equation by 4:

(4 * h) - (3 * o) = 9/4

Now, we have the following system of equations:

(79 * h) - (61 * o) = 9
(4 * h) - (3 * o) = 9/4

We can solve this system using the method of substitution or elimination. Let's use the method of elimination.

First, we can multiply the second equation by 16 to eliminate the variable o:

(64 * h) - (48 * o) = 9

Now, we can subtract the second equation from the first equation to eliminate the variable o:

(79 * h) - (61 * o) - ((64 * h) - (48 * o)) = 9 - 9

This simplifies to:

(15 * h) + (13 * o) = 0

Now, we can solve for h using the first equation:

(79 * h) - (61 * o) = 9

Substitute the value of o from the previous equation:

(79 * h) - (61 * (-15/13 * h)) = 9

This simplifies to:

(79 * h) + (61 * (15/13 * h)) = 9

Now, we can solve for h:

h = 9 / (79 + (61 * (15/13)))

h = 9 / (79 + (61 * 15/13))

h = 9 / (79 + 465/13)

h = 9 / (79 + 35.76923076923077)

h = 9 / 114.76923076923077

h = 0.0784313725490196

Now, we can substitute the value of h into the first equation to solve for o:

(79 * 0.0784313725490196) - (61 * o) = 9

o = (79 * 0.0784313725490196 - 9) / -61

o = (6.200000000000001 - 9) / -61

o = -2.8 / -61

o = 0.0459016393442623

Therefore, the values of o and h are:

o = 0.0459016393442623
h = 0.0784313725490196

### Answer: o = 0.0459016393442623, h = 0.0784313725490196

Expected answer: {h: 63/4, o: 81/4}

Correct? No

Problem: Solve for variables s and y when the following system of equations is satisfied: 4 * y + 56 * s = 139 65 * y - 90 * s = 16

Mixtral 8x22B:

 Reasoning:

We have the following system of equations:

1) 4y + 56s = 139
2) 65y - 90s = 16

We can solve this system using the method of substitution or elimination. Let's use the method of elimination.

First, we can multiply equation 1 by 15 and equation 2 by 4 to make the coefficients of y equal:

1) 60y + 840s = 2085
2) 260y - 360s = 64

Now, we can add the two equations to eliminate y:

3) 320y + 480s = 2149

Next, we can multiply equation 1 by 16 and equation 2 by 5 to make the coefficients of s equal:

1) 64y + 896s = 2224
2) 325y - 450s = 80

Now, we can add the two equations to eliminate s:

4) 389y = 2304

Now, we can solve for y:

y = 2304 / 389 = <<2304/389=5.922879177377891>>5.922879177377891

Next, we can substitute the value of y back into equation 1 to solve for s:

4(5.922879177377891) + 56s = 139

23.691516689511564 + 56s = 139

56s = 139 - 23.691516689511564

56s = 115.30848331048844

s = 115.30848331048844 / 56 = <<115.30848331048844/56=2.059080059080059>>2.059080059080059

### Answer: s = 2.059080059080059, y = 5.922879177377891

Expected answer: {s: 8971/4000, y: 6703/2000}

Correct? No

Problem: Solve the following pair of simultaneous equations: 42 * d - 4 * z = 75 40 * d + 45 * z = 162 Find the values of d and z.

Mixtral 8x22B:

 Reasoning:

First, let's solve the first equation for d:

42d - 4z = 75
42d = 75 + 4z
d = (75 + 4z) / 42

Now, let's substitute this expression for d into the second equation:

40 * ((75 + 4z) / 42) + 45z = 162

Now, let's solve for z:

40 * (75 + 4z) / 42 + 45z = 162
(40 * 75 + 40 * 4z) / 42 + 45z = 162
(3000 + 160z) / 42 + 45z = 162
3000 + 160z = 162 * 42 - 45z * 42
3000 + 160z = 6804 - 1890z
3000 + 160z + 1890z = 6804
2050z = 6804 - 3000
2050z = 3804
z = 3804 / 2050
z = 1.855

Now, let's substitute this value of z back into the expression for d:

d = (75 + 4 * 1.855) / 42
d = (75 + 7.42) / 42
d = 82.42 / 42
d = 1.962

So, the values of d and z are:

d = 1.962
z = 1.855

### Answer: d = 1.962, z = 1.855

Expected answer: {d: 4023/2050, z: 1902/1025}

Correct? No

Problem: Determine the values of 'a' and 'o' from the following system of equations: (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75.

Mixtral 8x22B:

 Reasoning:
Let's solve the system of equations using substitution or elimination method.

Using elimination method:
Multiply the first equation by 6 and the second equation by 24 to eliminate 'o':

(6 * 42 * o) + (6 * 24 * a) = 6 * 142
(24 * 42 * a) + (24 * 6 * o) = 24 * 75

Now, subtract the second equation from the first equation:

(6 * 42 * o) - (24 * 6 * o) = 6 * 142 - 24 * 75

Simplify the equation:

(252 * o) - (144 * o) = 852 - 1800

108 * o = -948

Divide both sides by 108:

o = -948 / 108
o = -8.777777777777778

Now, substitute the value of 'o' in the first equation to find the value of 'a':

(42 * -8.777777777777778) + (24 * a) = 142

Simplify the equation:

-368.8888888888889 + 24 * a = 142

Add 368.8888888888889 to both sides:

24 * a = 510.8888888888889

Divide both sides by 24:

a = 510.8888888888889 / 24
a = 21.28695652173912

Therefore, the values of 'a' and 'o' are approximately 21.29 and -8.78, respectively.

### Answer: a ≈ 21.29, o ≈ -8.78

Expected answer: {a: 383/270, o: 347/135}

Correct? No

Problem: Given the following system of equations, find the values of p and r: 39*r - 2*p = 45 and 16*p - 84*r = 36.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

First, we can multiply the first equation by 42 to eliminate the variable r:

42*(39*r - 2*p) = 42*45
1638*r - 84*p = 1890

Next, we can multiply the second equation by 39 to eliminate the variable p:

39*(16*p - 84*r) = 39*36
576*p - 3276*r = 1404

Now, we can add the two equations to eliminate the variable r:

1638*r - 84*p + 576*p - 3276*r = 1890 + 1404
-2430*r + 492*p = 3294

Next, we can solve for p:

492*p = 3294 + 2430*r
p = (3294 + 2430*r)/492

Now, we can substitute this expression for p back into the first equation to solve for r:

39*r - 2*((3294 + 2430*r)/492) = 45
39*r - (6588 + 4860*r)/492 = 45
19236*r - 6588 - 4860*r = 22140
14376*r = 28728
r = 2

Now that we have the value of r, we can substitute it back into the expression for p to find its value:

p = (3294 + 2430*2)/492
p = 816/492
p = 1.66

Therefore, the values of p and r are p = 1.66 and r = 2.

### Answer: p = 1.66, r = 2

Expected answer: {p: 216/19, r: 33/19}

Correct? No

Problem: Given the following system of equations, solve for the values of 'd' and 'w': 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58

Mixtral 8x22B:

 Reasoning:

First, let's solve equation 1 for 'd':

(23 * d) = 7 + (52 * w)
d = (7 + 52w) / 23

Now, let's substitute this expression for 'd' into equation 2:

(64 * w) - (8 * ((7 + 52w) / 23)) = 58

Now, let's solve for 'w':

(64 * w) - (8 * (7 + 52w) / 23) = 58
(64 * w) - (56/23) - (416w/23) = 58
(64 * w) - (416w/23) = 58 + (56/23)
(1472w - 416w) / 23 = 58 + (56/23)
(1056w) / 23 = 58 + (56/23)
1056w = 58 * 23 + 56
1056w = 1334 + 56
1056w = 1390
w = 1390 / 1056
w = 1.316

Now, let's substitute the value of 'w' back into the expression for 'd':

d = (7 + 52w) / 23
d = (7 + 52 * 1.316) / 23
d = (7 + 68.432) / 23
d = 75.432 / 23
d = 3.28

So, the values of 'd' and 'w' are approximately 3.28 and 1.316, respectively.

### Answer: d ≈ 3.28, w ≈ 1.316

Expected answer: {d: 433/132, w: 695/528}

Correct? No

Problem: Solve the following system of equations for the values of n and z: (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

First, let's solve the first equation for z:

z = (184 - 60n) / 71

Now, let's substitute this expression for z into the second equation:

52 * ((184 - 60n) / 71) - 47n = 19

Now, let's solve for n:

52 * (184 - 60n) - 47 * 71n = 19 * 71

8528 - 3120n - 3337n = 1349

-6457n = -7179

n = 7179 / 6457

Now, let's substitute the value of n back into the expression for z:

z = (184 - 60 * (7179 / 6457)) / 71

z = (184 - 430740 / 6457) / 71

z = (184 - 66.7) / 71

z = 117.3 / 71

z = 1.65

So, the solution to the system of equations is n = 7179 / 6457 and z = 1.65.

### Answer: n = 7179 / 6457, z = 1.65

Expected answer: {n: 8219/6457, z: 9788/6457}

Correct? No

Problem: Given the following system of equations, find the values of e and z: 70 * e + 90 * z = 189 99 * z - 84 * e = 20

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

Using the elimination method, we can multiply the first equation by 84 and the second equation by 70 to eliminate e:

(70 * 84) * e + (90 * 84) * z = 189 * 84
(99 * 70) * z - (84 * 70) * e = 20 * 70

This simplifies to:

5880 * e + 7560 * z = 15996
6930 * z - 5880 * e = 1400

Adding the two equations, we get:

14490 * z = 17396

Dividing both sides by 14490, we get:

z = 17396 / 14490

Now, we can substitute the value of z back into one of the original equations to find the value of e.

Using the first equation:

70 * e + 90 * (17396 / 14490) = 189

Simplifying, we get:

70 * e + 104.37 = 189

Subtracting 104.37 from both sides, we get:

70 * e = 84.63

Dividing both sides by 70, we get:

e = 84.63 / 70

Therefore, the values of e and z are:

e = 1.21
z = 1.2

### Answer: e = 1.21, z = 1.2

Expected answer: {e: 1879/1610, z: 1234/1035}

Correct? No

Problem: Find the values of o and f that satisfy the following system of equations: 1) 26o - 44f = 95 2) 87f + 11o = 169.

Mixtral 8x22B:

 Reasoning:

First, we can solve equation 1 for o:

o = (95 + 44f) / 26

Next, we can substitute this expression for o into equation 2:

87f + 11((95 + 44f) / 26) = 169

Now, we can solve for f:

87f + (11 \* 95) / 26 + (11 \* 44f) / 26 = 169

87f + 427.3076923076923 / 26 + 484f / 26 = 169

(87f + 484f) / 26 + 427.3076923076923 / 26 = 169

1351f / 26 + 427.3076923076923 / 26 = 169

1351f + 427.3076923076923 = 169 \* 26

1351f + 427.3076923076923 = 4394

1351f = 4394 - 427.3076923076923

1351f = 3966.692307692308

f = 3966.692307692308 / 1351

f = 2.936

Now that we have the value of f, we can substitute it back into the expression for o:

o = (95 + 44 \* 2.936) / 26

o = (95 + 129.264) / 26

o = 224.264 / 26

o = 8.625538461538462

Therefore, the values of o and f that satisfy the system of equations are o = 8.625538461538462 and f = 2.936.

### Answer: o = 8.625538461538462, f = 2.936

Expected answer: {f: 3349/2746, o: 15701/2746}

Correct? No

Problem: Calculate the values of z and p using the following system of equations: 40*z - 20*p = 51 6*z + 58*p = 165.

Mixtral 8x22B:

 Reasoning: To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.

First, we can multiply the first equation by 3 to make the coefficients of z in both equations equal:

120*z - 60*p = 153

Now, we can subtract the second equation from this new equation to eliminate z:

(120*z - 60*p) - (6*z + 58*p) = 153 - 165

114*z - 118*p = -12

Now, we can solve for p:

p = (114*z + 12) / 118

Next, we can substitute this expression for p back into the first equation to solve for z:

40*z - 20*((114*z + 12) / 118) = 51

Simplifying this equation, we get:

40*z - (2280*z + 240) / 118 = 51

Multiplying both sides by 118 to clear the fraction, we get:

4720*z - 2280*z - 240 = 6018

Simplifying further, we get:

2440*z = 6258

Dividing both sides by 2440, we get:

z = 6258 / 2440

Simplifying this fraction, we get:

z = 2.5647

Now, we can substitute this value of z back into the expression for p to find its value:

p = (114*2.5647 + 12) / 118

Simplifying this expression, we get:

p = 2.9999

Therefore, the values of z and p are approximately 2.56 and 3.00, respectively.

### Answer: z ≈ 2.56, p ≈ 3.00

Expected answer: {p: 3147/1220, z: 3129/1220}

Correct? No

Problem: Find the values of s and f from the given system of equations: (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93.

Mixtral 8x22B:

 Reasoning:

Let's solve the system of equations using the substitution or elimination method.

Using the elimination method, we can multiply the second equation by 8.9 to eliminate f:

(8.9 * 3 * f) + (8.9 * 10 * s) = 8.9 * 93

26.7 * f + 89 * s = 827.7

Now, we can subtract the first equation from this new equation to eliminate s:

(26.7 * f + 89 * s) - (71 * s - 89 * f) = 827.7 - 5

26.7 * f + 89 * s - 71 * s + 89 * f = 822.7

Combining like terms, we get:

115.7 * f + 18 * s = 822.7

Now, we can multiply the first equation by 18 to eliminate s:

(18 * 71 * s) - (18 * 89 * f) = 18 * 5

1278 * s - 1602 * f = 90

Now, we can subtract this new equation from the previous equation to eliminate s:

(115.7 * f + 18 * s) - (1278 * s - 1602 * f) = 822.7 - 90

115.7 * f + 18 * s - 1278 * s + 1602 * f = 732.7

Combining like terms, we get:

1717.7 * f - 1260 * s = 732.7

Now, we have a system of two equations with two variables:

115.7 * f + 18 * s = 822.7
1717.7 * f - 1260 * s = 732.7

We can solve this system using the substitution or elimination method. Let's use the elimination method again.

Multiply the first equation by 70 to eliminate s:

(70 * 115.7 * f) + (70 * 18 * s) = 70 * 822.7

8099 * f + 1260 * s = 57589

Now, we can subtract the second equation from this new equation to eliminate s:

(8099 * f + 1260 * s) - (1717.7 * f - 1260 * s) = 57589 - 732.7

8099 * f + 1260 * s - 1717.7 * f + 1260 * s = 56856.3

Combining like terms, we get:

6381.3 * f = 56856.3

Now, we can solve for f:

f = 56856.3 / 6381.3

f = 8.91

Now that we have the value of f, we can substitute it back into one of the original equations to solve for s. Let's use the first equation:

(71 * s) - (89 * 8.91) = 5

71 * s - 793.99 = 5

Now, we can solve for s:

71 * s = 5 + 793.99

71 * s = 798.99

s = 798.99 / 71

s = 11.25

Therefore, the values of s and f are:

s = 11.25
f = 8.91

### Answer: s = 11.25, f = 8.91

Expected answer: {f: 6553/1103, s: 8292/1103}

Correct? No