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 8x7B:

 To solve for the values of variables q and s, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 3 and the second equation by 91/30 to make the coefficients of s the same in both equations:

1. (120 * s) - (273 * q) = 111
2. (329.7 * s) + (36.4 * q) = 111.9

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

(329.7 * s) + (36.4 * q) - (120 * s) + (273 * q) = 111.9 - 111

This simplifies to:

239.7 * s + 236.6 * q = 0.9

Now, let's divide the entire equation by 0.9:

s + q = 1

Now, let's solve for q:

q = 1 - s

Substitute this expression for q into the first equation:

(40 * s) - (91 * (1 - s)) = 37

This simplifies to:

131 * s = 128

Now, let's solve for s:

s = 128 / 131

Substitute this value of s into the expression for q:

q = 1 - (128 / 131)

Now, let's simplify the expressions for s and q:

s = 0.9771
q = 0.0229

### Answer: The values of variables q and s are 0.0229 and 0.9771, respectively.

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 8x7B:

 To solve the system of equations for the values of b and m, we can first multiply the second equation by 2 and add it to the first equation to eliminate the variable b:

(79*m - 6*b = 48) x 2
158*m - 12*b = 96

Adding this to the first equation:

(4*b + 44*m = 180)
+ (158*m - 12*b = 96)
-----------------
154*m + (-8*b) = 276

Now, we can solve for m by dividing both sides by 154:

m = (276 + 8*b) / 154

Next, we can substitute this expression for m into either equation to solve for b. We'll use the first equation:

4*b + 44*(276 + 8*b) / 154 = 180

Multiplying both sides by 154 to eliminate the fraction:

616*b + 44*276 = 23760

Simplifying:

616*b = 22488

Dividing both sides by 616:

b = 36.5

Now, we can substitute this value of b into the expression for m:

m = (276 + 8*36.5) / 154

Simplifying:

m = 2.5

So, the solution to the system of equations is b = 36.5 and m = 2.5.

### Answer: b = 36.5, m = 2.5

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 8x7B:

 To solve this system of equations, we can use the substitution or elimination method. Here, I will use the elimination method.
First, let's multiply the first equation by 29 and the second equation by 15 to make the coefficients of g the same in both equations:

(42 * o - 15 * g) * 29 = 28 * 29
(47 * o + 29 * g) * 15 = 141 * 15

This gives us:

1218 * o - 435 * g = 812
693 * o + 435 * g = 2115

Now, let's add these two equations:

1218 * o - 435 * g + 693 * o + 435 * g = 812 + 2115
1911 * o = 2927

Now, let's solve for o:

o = 2927 / 1911
o = 1.5308

Now, let's substitute this value of o into the first equation:

42 * 1.5308 - 15 * g = 28
63.8736 - 15 * g = 28

Now, let's solve for g:

15 * g = 63.8736 - 28
15 * g = 35.8736
g = 35.8736 / 15
g = 2.3916

So, the solution to the system of equations is o = 1.5308 and g = 2.3916.
### Answer: o = 1.5308, g = 2.3916

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 8x7B:

 To solve for v and o, we can first multiply the first equation by 6 to eliminate v in the second equation.

12v - 6o = 21
6(12v - 6o) = 6(21)
72v - 36o = 126

Now, we can subtract the first equation from the new equation to solve for o.

72v - 36o = 126
- (12v - 6o = 21)
60v - 30o = 105

Divide the new equation by 30 to solve for o.

60v - 30o = 105
30v - 15o = 52.5
o = (30v - 52.5) / 15

Now, we can substitute o into the first equation to solve for v.

12v - 6o = 21
12v - 6((30v - 52.5) / 15) = 21
12v - 6(20v - 52.5/5) = 21
12v - 6(20v - 10.5) = 21
12v - 120v + 63 = 21
-108v = -42
v = -42 / -108
v = 0.39

Now, we can substitute v into the equation for o.

o = (30v - 52.5) / 15
o = (30(0.39) - 52.5) / 15
o = (11.7 - 52.5) / 15
o = -40.8 / 15
o = -2.72

### Answer: v = 0.39, o = -2.72

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 8x7B:

 To find the values of f and g, we can use the substitution or elimination method. Here, I'll use the elimination method.

First, let's multiply the first equation by 2 and the second equation by 75 to make the coefficients of g the same in both equations:

150f + 50g = 276
150f + 6750g = 10725

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

6700g = 10449

Next, divide both sides by 6700:

g = 10449 / 6700
g = 1.56

Now, let's substitute g = 1.56 into the first equation:

75f + 25\*1.56 = 138
75f + 39 = 138

Subtract 39 from both sides:

75f = 99

Finally, divide both sides by 75:

f = 99 / 75
f = 1.32

### Answer: f = 1.32, g = 1.56

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 8x7B:

 To solve the system of equations, we first need to eliminate one of the variables. We can do this by multiplying the first equation by 79 and the second equation by 14 and then adding the resulting equations together. This will eliminate the variable y.

194 \* 79 = 4 \* y \* 79 + 14 \* n \* 79
7 \* 14 = 65 \* n \* 14 - 79 \* y \* 14

This gives us:
15266 = 316 \* y + 1006 \* n
98 = 910 \* n - 1106 \* y

Now, we can solve for n by multiplying the first equation by 1106 and the second equation by 316 and then adding the resulting equations together. This will eliminate the variable y.

15266 \* 1106 = 316 \* y \* 1106 + 1006 \* n \* 1106
98 \* 316 = 910 \* n \* 316 - 1106 \* y \* 316

This gives us:
16858756 = 100276 \* n

Now, we can solve for n by dividing both sides of the equation by 100276

n = 16858756 / 100276
n = 168

Now we can substitute n = 168 into the first equation to solve for y

194 = 4 \* y + 14 \* 168
194 = 4 \* y + 2352

Now, we can solve for y by subtracting 2352 from both sides of the equation

4 \* y = 194 - 2352
4 \* y = -2158

Now, we can solve for y by dividing both sides of the equation by 4

y = -2158 / 4
y = -539.5

However, y should be a positive integer, so the system of equations has no solution.
### Answer: No solution.

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 8x7B:

 To solve for l and g, we can first simplify the first equation by dividing both sides by 13 (since 28 and 26 are both multiples of 13):

11 = g + 2l

Next, we can solve the second equation for l:

l = (53g + 6) / 41

Now, we can substitute the expression for l from the second equation into the first equation:

11 = g + 2((53g + 6) / 41)

Multiplying both sides by 41 to eliminate the fraction, we get:

451 = 41g + 2(53g + 6)

Simplifying, we get:

451 = 41g + 106g + 12

Combining like terms, we get:

451 = 147g + 12

Subtracting 12 from both sides, we get:

439 = 147g

Dividing both sides by 147, we get:

g = 439 / 147

Simplifying, we get:

g = 13/3

Since g must be a whole number, there is no solution for g and l that satisfies both equations.

### Answer: There is no solution for g and l that satisfies both equations.

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 8x7B:

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

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

1) 140 * p + 392 * y = 630
2) 5016 * p + 412 * y = 5488

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

(5016 * p + 412 * y) - (140 * p + 392 * y) = 5488 - 630

This simplifies to:

4876 * p = 4858

Now, let's solve for p:

p = 4858 / 4876
p = 1.00123

Now, let's substitute the value of p back into the first equation to solve for y:

20 * 1.00123 + 56 * y = 90

This simplifies to:

56 * y = 90 - 20.0246

Now, let's solve for y:

y = (90 - 20.0246) / 56
y = 1.346

So, the solution to the system of equations is p = 1.00123 and y = 1.346.
### Answer: p = 1.00123, y = 1.346

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 8x7B:

 To solve for the variables k and d, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 6 and the second equation by 22 to make the coefficients of d the same in both equations:

72*6*k - 22*6*d = 17*6
132*d + 69*66*k = 96*22

This gives us:

432*k - 132*d = 102
132*d + 4638*k = 2112

Now, let's add these two equations:

4670*k = 2213.2

Dividing both sides by 4670, we get:

k = 2213.2 / 4670
k = 0.4742

Now, let's substitute k = 0.4742 into the first equation:

72*0.4742 - 22*d = 17
33.9024 - 22*d = 17

Subtracting 33.9024 from both sides, we get:

-22*d = -16.9024

Dividing both sides by -22, we get:

d = -16.9024 / -22
d = 0.7683

So, the values of the variables k and d are approximately 0.4742 and 0.7683, respectively.
### Answer: k ≈ 0.4742, d ≈ 0.7683.

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 8x7B:

 To solve this system of equations, we first need to eliminate one of the variables. We can do this by multiplying the second equation by 11/2 to make the coefficients of h the same in both equations:

10*d + 14*h = 91
110*d/2 + 77*h/2 = 91*11/2

This gives us:

110*d/2 + 77*h/2 = 533/2

Now, we can subtract the first equation multiplied by 77/2 from the second equation:

(110*d/2 + 77*h/2) - (77*(73*h - 33*d))/2 = 533/2

This simplifies to:

110*d/2 - 2421*h/2 = 533/2 - 39117/2

Multiplying both sides by 2 to get rid of the fractions:

110*d - 2421*h = 533 - 39117

110*d - 2421*h = -38584

Now, we can solve for one of the variables. Let's solve for d:

d = (2421*h + 38584)/110

Now, we can substitute this expression for d into the first equation:

73*h - 33*(2421*h + 38584)/110 = 48

Solving for h:

73*h - 7263*h/11 - 12041*h/11 = 48

-7263*h/11 + 73*h - 12041*h/11 = 48

-19304*h/11 = 48 - 73

-19304*h/11 = -25

h = -25 \* 11 / 19304

h = -275 / 2411

Now, we can substitute this value of h into the expression for d:

d = (2421\*(-275/2411) + 38584)/110

d = (678750 - 38584)/110\*2411

d = 640166/26521

d = 24.13 (rounded to two decimal places)

However, since d represents the number of clips, it must be a whole number. Therefore, the solution d = 24.13 is not valid.

Instead, we can conclude that there is no solution to this system of equations where d and h are both whole numbers.
### Answer: No solution where d and h are both whole numbers.

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 8x7B:

 To solve this system of equations, we first multiply the first equation by 43 and the second equation by 44, to eliminate the variable e in the second equation:

1) 43 * 43 * q - 43 * 44 * e = 43 * 29
2) 30 * 44 * q + 43 * 44 * e = 130 \* 44

Adding both equations, we get:

(43^2 * q) - (43 * 44 * e) + (30 * 44 * q) + (43 * 44 * e) = 43 \* 29 + 130 \* 44

Simplifying, we get:

43^2 * q + 30 \* 44 * q = 43 \* 29 + 130 \* 44

Now, we factor out q:

q \* (43^2 + 30 \* 44) = 43 \* 29 + 130 \* 44

Solving for q:

q = (43 \* 29 + 130 \* 44) / (43^2 + 30 \* 44)
q = (1207 + 5720) / (1849 + 1320)
q = 6927 / 3169
q = 2.185

Now, we substitute the value of q into the first equation:

43 \* 2.185 - 44 \* e = 29

Solving for e:

e = (43 \* 2.185 - 29) / 44
e = (93.605 - 29) / 44
e = 64.605 / 44
e = 1.468

So, the solution to the system of equations is q = 2.185 and e = 1.468.
### Answer: q = 2.185, e = 1.468

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 8x7B:

 To solve for r and a, we can use the substitution or elimination method. Here, I'll use the elimination method.

First, let's multiply the second equation by 7 to make the coefficients of r in both equations the same:

109 * 7 = 763 = (37 * a) + (6 * r)

Now, let's add the two equations:

53 + 763 = 816 = (89 * r) - (74 * a) + (37 * a) + (6 * r)
816 = (89 * r) + (6 * r) - (74 * a) + (37 * a)
816 = (89 + 6) * r - (74 - 37) * a
816 = 95 * r - 37 * a

Now, let's multiply the first equation by 37 and the second equation by 89, and then subtract the second equation from the first:

53 * 37 = 1961 = (89 * r) - (74 * a)
109 * 89 = 9681 = (37 * a) + (6 * r)

1961 - 9681 = -7720 = (89 * r) - (74 * a) - (37 * a) - (6 * r)
1961 - 9681 = -7720 = (89 - 6) * r - (74 + 37) * a
1961 - 9681 = -7720 = 83 * r - 111 * a

Now, we can use the first equation to solve for r:

83 * r = 1961 + 7720
83 * r = 9681
r = 9681 / 83
r = 116.5783

Now, we can substitute r into the first equation to solve for a:

53 = ((89 * 116.5783) - (74 * a))
53 = 10342.5299 - 74 * a
74 * a = 10342.5299 - 53
a = (10342.5299 - 53) / 74
a = 139.5783

So, the values of r and a are approximately 116.5783 and 139.5783, respectively.
### Answer: r ≈ 116.5783, a ≈ 139.5783

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 8x7B:

 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 can write the equation: 42w\_g + 12w\_q = 169

From the second equation, we can write the equation: 12w\_q - 50w\_g = 19

Now, we can solve this system of equations.

First, let's isolate w\_g in the second equation: w\_g = (12w\_q - 19) / 50

Now, substitute this expression for w\_g into the first equation: 42((12w\_q - 19) / 50) + 12w\_q = 169

Solve for w\_q: 252w\_q - 387 + 300w\_q = 8450
552w\_q = 8837
w\_q = 8837 / 552
w\_q = 16.01 (rounded to two decimal places)

Now, substitute w\_q = 16.01 into the equation w\_g = (12w\_q - 19) / 50:
w\_g = (12*16.01 - 19) / 50
w\_g = 1.21

So, the weight of one unit of 'g' is 1.21 kg and the weight of one unit of 'q' is 16.01 kg.

Now, let's find the quantities of 'g' and 'q' that Natalia has.

From the first equation, we have: 42*1.21 + 12*16.01 = 50.82 + 192.12 = 242.94 kg

Since Natalia sold 42 units of 'g' and 12 units of 'q', the total quantity of grains she sold is 42 + 12 = <<42+12=54>>54 units.

### Answer: g = 1.21 kg, q = 16.01 kg, and Natalia sold a total of 54 units of grains in April.

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 8x7B:

 To find the values of s and v, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 2 and the second equation by 11/4 to make the coefficients of s the same in both equations:

2*(37*s - 11*v) = 2*54
11/4*(82*s - 62*v) = 11/4*41

This gives us:

74*s - 22*v = 108
195.5*s - 169.25*v = 114.75

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

(195.5*s - 169.25*v) - (74*s - 22*v) = 114.75 - 108

This simplifies to:

121.5*s - 147.25*v = 6.75

Now, let's multiply the first equation by 147.25/121.5 to make the coefficients of s the same in both equations:

147.25/121.5 * (74*s - 22*v) = 6.75 * 147.25/121.5

This simplifies to:

s - 1.875*v = 0.55

Now, let's solve for v:

v = (s - 0.55) / 1.875

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

37*s - 11*(s - 0.55) / 1.875 = 54

Solving this equation gives us:

s = 1.5

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

v = (1.5 - 0.55) / 1.875

v = 0.5

So, the values of s and v are 1.5 and 0.5, respectively.

### Answer: s = 1.5, v = 0.5

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 8x7B:

 To find the values 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 2 and the second equation by 1 to make the coefficients of c the same in both equations:

2 \* (41 \* c + 65 \* z = 151) -> 82 \* c + 130 \* z = 302
1 \* (78 \* z - 48 \* c = 48) -> 78 \* z - 48 \* c = 48

Now, let's add the two equations:

(82 \* c + 130 \* z) + (78 \* z - 48 \* c) = 302 + 48
82 \* c + 130 \* z + 78 \* z - 48 \* c = 350
34 \* c + 208 \* z = 350

Now, let's divide the equation by 34:

(34 \* c + 208 \* z) / 34 = 350 / 34
c + 6.12 \* z = 10.29

Now, let's solve for z:

6.12 \* z = 10.29 - c
z = (10.29 - c) / 6.12

Now, let's substitute z into the first equation:

41 \* c + 65 \* ((10.29 - c) / 6.12) = 151
41 \* c + 108.29 - 65 \* c / 6.12 = 151
-24 \* c = -57.29
c = 57.29 / 24 = 2.4

Now, let's substitute c into the equation for z:

z = (10.29 - 2.4) / 6.12
z = 7.89 / 6.12
z = 1.29

So, the values for c and z are 2.4 and 1.29, respectively.
### Answer: c = 2.4, z = 1.29

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 8x7B:

 To solve for the values of c and i, we can use the substitution or elimination method of solving systems of linear equations. Here, I will use the elimination method.

First, let's multiply the first equation by 7 and the second equation by 91 to make the coefficients of i the same in both equations:

60 * c - 91 * i = 7 becomes 420 * c - 637 * i = 49

7 * i + 76 * c = 148 becomes 632 * c - 148 * i = 1336

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

(632 * c - 148 * i) - (420 * c - 637 * i) = 1336 - 49

This simplifies to:

212 * c + 489 * i = 1287

Now, let's multiply the first equation by 489 and the second equation by 60 to make the coefficients of c the same in both equations:

60 * c - 91 * i = 7 becomes 29340 * c - 4359 * i = 426

7 * i + 76 * c = 148 becomes 456 * c - 7 * i = 8880

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

(456 * c - 7 * i) - (29340 * c - 4359 * i) = 8880 - 426

This simplifies to:

-28884 * c + 4352 * i = 8454

Now, let's multiply this equation by 5 and add it to the previous equation:

(212 * c + 489 * i) + 5 * (-28884 * c + 4352 * i) = 1287 + 5 * 8454

This simplifies to:

-149188 * c + 21760 * i = 45270

Now, let's divide both sides by -149188 to solve for c:

c = -21760 * i / 149188

Now, let's substitute this value of c into the first equation:

60 * (-21760 * i / 149188) - 91 * i = 7

This simplifies to:

-870.41 * i = 7

Now, let's divide both sides by -870.41 to solve for i:

i = 7 / -870.41

Now, let's substitute this value of i into the equation for c:

c = -21760 * (7 / -870.41) / 149188

Now, let's simplify this expression to find the values of c and i:

c = 0.000085

i = -0.008

### Answer: c = 0.000085, i = -0.008

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 8x7B:

 To solve for e and v, we can use the substitution or elimination method. 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 the same in both equations:

1) 71*v - 37*e = 69 becomes 2897*v - 1517*e = 2573
2) 41*e + 76*v = 184 becomes 1517*e + 2859*v = 6712

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

(1517*e + 2859*v) - (2897*v - 1517*e) = 6712 - 2573
1517*e + 2859*v - 2897*v + 1517*e = 4139
-38*v = 4139

Now, let's solve for v:

v = 4139 / -38
v = -108.92 (rounded to two decimal places)

Now, let's substitute v = -108.92 into the first equation:

71*(-108.92) - 37*e = 69
-7682.52 - 37*e = 69

Now, let's solve for e:

-37*e = 69 + 7682.52
-37*e = 7751.52
e = 7751.52 / -37
e = -209.5 (rounded to one decimal place)

So, the values of e and v that satisfy the two simultaneous linear equations are:
### Answer: e = -209.5, v = -108.92

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 8x7B:

 To solve for the values of 'd' and 'v' in this system of equations, we can first multiply the first equation by 26 and the second equation by 69 to eliminate 'v' from the second equation and 'd' from the first equation:

26 \* (25v + 69d) = 26 \* 113
42 \* (26d + 42v) = 69 \* 85

This gives us:

650v + 1834d = 2918
1762d + 2918v = 5865

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

1762d - 650d = 5865 - 2918
1112d = 2947
d = 2947 / 1112
d = 2.65

Now, we can substitute the value of 'd' into the first equation to solve for 'v':

25v + 69 \* 2.65 = 113
25v = 113 - 183.85
25v = -70.85
v = -70.85 / 25
v = -2.83

### Answer: d = 2.65, v = -2.83

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 8x7B:

 To solve for g and z, we can first multiply the first equation by 3 and the second equation by 91, so that the coefficients of z in both equations are equal:

3*(43 * z - 91 * g) = 3*33
91*(72 * g - 3 * z) = 91*68

This gives us:

129 * z - 273 * g = 99
6512 * g - 273 * z = 6216

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

129 * z - 273 * g + 6512 * g - 273 * z = 99 + 6216
6239 * g = 6315

g = 6315 / 6239 = 1.013

Now, we can substitute this value of g into the first equation to find z:

43 * z - 91 * 1.013 = 33
43 * z = 33 + 91 * 1.013
43 * z = 33 + 92.343
43 * z = 125.343
z = 125.343 / 43 = 2.915

So, the solution is g = 1.013 and z = 2.915.
### Answer: g = 1.013, z = 2.915

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 8x7B:

 To solve this system of equations, we can first multiply the second equation by 2 to eliminate $f$ when we add the two equations together:

50c + 12f = 92
72c - 42f = 68

Adding these two equations gives:

122c = 160

Dividing both sides by 122 gives:

c = 160/122 = 10/8 = 1.25

Now we can substitute $c=1.25$ into the first equation to find $f$:

50(1.25) + 12f = 92

62.5 + 12f = 92

12f = 92 - 62.5

12f = 29.5

f = 29.5/12 = 2.45833333333

So Natalia sold 1.25 cherries and 2.46 figs. However, since we cannot have a fraction of a fruit, it is likely that the original problem has some errors or approximations. If we round the number of cherries and figs to the nearest whole number, we get 1 cherry and 2 figs, but this does not satisfy either of the original equations.

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 8x7B:

 To solve for u and d, we can first add the two equations to eliminate one variable:

87u - 75d + 85d - 82u = 7 + 54
-5u + 10d = 61
5u = 10d - 61
u = (10d - 61)/5

Now, we can substitute this expression for u into one of the original equations to solve for d. We'll use the first equation:

87(10d - 61)/5 - 75d = 7

To simplify, we can first multiply both sides by 5:

87(10d - 61) - 375d = 35

Expanding and simplifying further, we get:

870d - 5207 - 375d = 35
495d = 5242
d = 5242 / 495
d = 10.59

Since d must be a whole number, there is no solution for u and d that satisfies both equations.
### Answer: There is no solution for u and d that satisfies both equations.

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 8x7B:

 Reasoning: We have two equations here:

1) 75a - 4i = 42
2) 10i + 13a = 160

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

First, let's multiply the first equation by 13 and the second equation by 4:

1) 975a - 52i = 546
2) 40i + 52a = 640

Now, let's add both equations:

(975a - 52i) + (40i + 52a) = 546 + 640
1027a = 1186

Now, let's divide both sides by 1027:

a = 1186 / 1027
a = 2

Now, let's substitute a = 2 into the first equation:

75*2 - 4i = 42
150 - 4i = 42

Now, let's subtract 150 from both sides:

-4i = -108

Now, let's divide both sides by -4:

i = -108 / -4
i = 27

### Answer: The values of i and a are 27 and 2, respectively.

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 8x7B:

 To solve this system of equations, we first need to eliminate one of the variables. We can do this by multiplying the second equation by 37/

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 8x7B:

 To solve for k and p, we can first isolate one variable in one of the equations and then substitute that expression into the other equation to solve for the other variable.

Let's isolate p in the first equation:

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

Now, we can substitute this expression for p into the second equation:

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

Solving this equation for k, we get:

k = 3

Substituting k = 3 into the expression for p, we get:

p = (48 \* 3 - 37) / 30
p = 131 / 30
p = 4.3\overline{6}

However, p must be an integer, so there is no solution for this system of equations.
### Answer: No solution (k, p) exists for this system of equations.

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 8x7B:

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

First, let's multiply the first equation by 53 and the second equation by 75 to make the coefficients of v equal in both equations:

1. 53(75v - 69f) = 14 \* 53
75v - 69f = 742

2. 75(46f + 53v) = 110 \* 75
46f + 53v = 825

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

(46f + 53v) - (75v - 69f) = 825 - 742
46f - 22f = 83
24f = 83
f = 83 / 24
f = 3.45833

Since f is not a whole number, there is no solution for this system of equations with integer values for f and v.

### Answer: There is no solution for this system of equations with integer values for f and v.

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 8x7B:

 We can solve this system of equations using substitution or elimination method. Here, I will use elimination method.
First, let's multiply the first equation by 10 to make the coefficients of o's the same in both equations:
70 * o + 130 * g = 1310
Now, let's subtract the second equation from this new equation:
(70 * o + 130 * g) - (89 * g - 70 * o) = 1310 - 37
80 * o + 41 * g = 1273
Now, let's multiply the second equation by 41/89 (approximately 0.4606) to make the coefficients of g's the same in both equations:
34.426 * g - 32.202 * o = 17.456
Now, let's subtract this new equation from the previous equation:
(80 * o + 41 * g) - (34.426 * g - 32.202 * o) = 1273 - 17.456
47.574 * o + 7.574 * g = 1255.544
Now, let's divide the second equation by 7.574 (approximately 0.1657) to solve for o:
o = (1255.544 - 7.574 * g) / 47.574
Now, let's substitute this value of o into the first equation to solve for g:
7 * (1255.544 - 7.574 * g) / 47.574 + 13 * g = 131
g = 1
Now, let's substitute this value of g into the equation for o:
o = (1255.544 - 7.574 * 1) / 47.574
o = 26
### Answer: o = 26, g = 1

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 8x7B:

 To solve this system of equations, we can first multiply the second equation by 2 to eliminate the variable $d$ when we add the two equations together:

$88*d - 60*k = 38$
$66*k - 22*d = 92$

Adding the two equations gives:

$22*k = 130$

Dividing both sides by 22, we get:

$k = \frac{130}{22} = \frac{65}{11}$

Substituting this value of $k$ into the first equation, we get:

$88*d - 60*\frac{65}{11} = 38$

$88*d = 38 + 60*\frac{65}{11} = 38 + 30*5 = 38 + 150 = 188$

Dividing both sides by 88, we get:

$d = \frac{188}{88} = \frac{47}{22}$

Therefore, the solution to the system of equations is:

### Answer: d = 47/22, k = 65/11.

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 8x7B:

 To solve for y and z, we can use the substitution or elimination method. Here, I will use the elimination method.
First, let's multiply the second equation by 36 to make the coefficients of y the same in both equations:
2 * z + 82 * y = 96 -> 72 * z + 2952 * y = 3456
Now, let's subtract the first equation from the second one:
(72 * z + 2952 * y) - (24 * z + 72 * y) = 3456 - 139
58 * z = 3317
z = 3317 / 58
z = 57
Now, let's substitute z = 57 into the first equation:
24 * 57 + 72 * y = 139
1368 + 72 * y = 139
72 * y = 139 - 1368
72 * y = -1229
y = -1229 / 72
y = -17.0694444444
However, y should be a whole number because it represents the number of clips sold. This means that the system of equations has no solution with whole numbers for y and z.
### Answer: The system of equations has no solution with whole numbers for y and z.

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 8x7B:

 To solve the system of equations, we first need to eliminate one of the variables. We can do this by multiplying the first equation by 30 and the second equation by 29, so that the coefficients of v in both equations are equal:

870o - 29v = 30
232v + 870o = 2618

Adding these two equations, we get:

870o - 29v + 232v + 870o = 30 + 2618
203v = 2648

Dividing both sides by 203, we get:

v = 2648 / 203
v = 13.05

Now, we can substitute this value of v into the first equation to find the value of o:

87o - 29(13.05) = 1
87o = 1 + 29(13.05)
87o = 1 + 378.45
87o = 379.45

Dividing both sides by 87, we get:

o = 379.45 / 87
o = 4.36

So, the solution to the system of equations is v = 13.05 and o = 4.36.
### Answer: v = 13.05, o = 4.36

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 8x7B:

 To solve the system of equations for h and p, we can first add the two equations to eliminate h:

(23 * h) - (46 * p) + (11 * p) + (23 * h) = 58 + 124
(46 * h) - (35 * p) = 182

Next, we can solve this equation for h:

h = (182 + 35 * p) / 46

Now, we can substitute this expression for h into either of the original equations to solve for p. We'll use the first equation:

(23 * ((182 + 35 * p) / 46)) - (46 * p) = 58

Solving this equation for p, we get:

p = 2

Substituting this value of p into the expression for h, we get:

h = (182 + 35 * 2) / 46
h = 10

So, the solution to the system of equations is h = 10 and p = 2.
### Answer: h = 10, p = 2

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 8x7B:

 To solve this system of equations, we can use the method of substitution or elimination. Here, I will use the elimination method.
First, we will multiply the first equation by 4 and the second equation by 6 to make the coefficients of f the same in both equations:
1) 76d + 24f = 480,
2) 540d - 252f = 414.

Now, we can subtract the second equation from the first to eliminate f:
(76d + 24f) - (540d - 252f) = 480 - 414
-464d = 66
d = 66 / -464 = -3/26

Now, we can substitute the value of d into the first equation to find f:
19(-3/26) + 6f = 120
-57/26 + 6f = 120
6f = 120 + 57/26
6f = 120 \* 26/26 + 57/26
6f = 3123/26
f = 3123/156
f = 20 1/13

However, since the problem asks for integer values of d and f, this problem has no solution.
### Answer: The problem has no solution with integer values of d and f.

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 8x7B:

 To solve this system of linear equations, we can use the method of elimination. First, let's multiply the first equation by 2 and the second equation by -1 to eliminate the variable r:

1) 84 * m + 110 * r = 254
2) -66 * m + 52 * r = -44

Adding these two equations together, we get:

(84 * m + 110 * r) + (-66 * m + 52 * r) = 254 + (-44)
18 * m = 210

Now, let's solve for m:

m = 210 / 18
m = 11.67 (rounded to two decimal places)

Now, let's substitute the value of m back into the first equation to solve for r:

42 * 11.67 + 55 * r = 127
484.74 + 55 * r = 127
55 * r = 127 - 484.74
55 * r = -357.74
r = -357.74 / 55
r = -6.5 (rounded to one decimal place)

So, the solution to the system of linear equations is m = 11.67 and r = -6.5.
### Answer: m = 11.67, r = -6.5

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 8x7B:

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

First, let's multiply the first equation by 71 and the second equation by 31 to make the coefficients of n the same in both equations:

31n * 71 + 64w * 71 = 120 * 71
57w * 31 + 71n * 31 = 173 * 31

This gives us:

2231n + 1984w = 8571
1767w + 2201n = 5363

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

(2231n + 1984w) - (1767w + 2201n) = 8571 - 5363

This simplifies to:

-234w = 3208

Now, let's divide both sides by -234 to isolate w:

w = 3208 / -234
w = -13.71

Since the number of clips must be a whole number, this problem has no solution.
### Answer: No solution (n, w) exists that satisfies the given 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 8x7B:

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

First, let's multiply the first equation by 77 and the second equation by 26 to make the coefficients of a the same in both equations:

1) 77(72a + 26u) = 77(112)
a*77*72 + u*77*26 = 8864

2) 26(76u - 77a) = 26(31)
u*26*76 - a*26*77 = 836

Now, let's add the two equations:

a*77*72 + u*77*26 = 8864
u*26*76 - a*26*77 = 836
----------------------
a*77*72 + u*77*26 + u*26*76 - a*26*77 = 8864 + 836
a*(77*72 - 26*77) + u*(77*26 + 26*76) = 9700

Now, we can solve for a and u:

a*(77*72 - 26*77) = 9700
a*(5321 - 1972) = 9700
a*3349 = 9700
a = 9700 / 3349
a = 2.895 (approximately)

u*(77*26 + 26*76) = 9700
u*(2002 + 1976) = 9700
u*3978 = 9700
u = 9700 / 3978
u = 2.438 (approximately)

So, the values of a and u are approximately 2.895 and 2.438, respectively.
### Answer: u ≈ 2.438, a ≈ 2.895

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 8x7B:

 To solve the system of equations for the values of b and n, we can first multiply the first equation by 3 to eliminate the variable n:

54n + 18b = 143
162n + 54b = 429

Then, add the new equation to the second equation:

(162n + 54b) + (87n - 93b) = 429 + 48
249n - 39b = 477

Now, we can divide both sides by -39 to isolate b:

b = (249n - 477) / -39
b = -6.384615...n + 12.230769...

Since b is a whole number, n must be a multiple of 39/6.384615... or approximately 6.13. The smallest multiple of 6.13 is 6, so we can test n = 6:

b = -6.384615...(6) + 12.230769...
b = -38 + 12
b = -26

Substitute b = -26 into the first equation:

54n + 18(-26) = 143
54n - 468 = 143
54n = 611
n = 611 / 54
n = 11.314815...

Since n is not a whole number, there is no solution for the system of equations with integer values of b and n.

### Answer: There is no solution for the system of equations with integer values of b and n.

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 8x7B:

 To solve this system of equations, we first need to eliminate one of the variables. We can do this by multiplying the first equation by 88/7 and adding it to the second equation:

(88/7)(53 \* e + 7 \* p) + 69 \* e - 88 \* p = 6
(88/7)(53 \* e) + (88/7)(7 \* p) + 69 \* e - 88 \* p = 6
(4416/7) \* e + 88 \* p + 69 \* e - 88 \* p = 6
(5072/7) \* e = 6
e = 6 / (5072/7)
e = 6 * (7/5072)
e = 42 / 3624
e = 1/86

Now that we have a value for e, we can substitute it back into either equation to find p. We'll use the first equation:

53 \* e + 7 \* p = 103
53 \* (1/86) + 7 \* p = 103
p = (103 - 53 \* (1/86)) / 7
p = (103 - 53 / 86) / 7
p = (103 - 1/2) / 7
p = (205 - 1) / 14
p = 204 / 14
p = 102 / 7

### Answer: e = 1/86 and p = 102/7

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 8x7B:

 To find the values of p and s that satisfy both equations, we can first solve one equation for one variable and then substitute that expression into the other equation.

Let's solve the first equation for p:

(18 \* p) - (7 \* s) = 21
(18 \* p) = 21 + (7 \* s)
p = (21 + (7 \* s)) / 18

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

((51 \* s) - (24 \* ((21 + (7 \* s)) / 18))) = 14

To solve for s, first multiply both sides by 18 to eliminate the fraction:

(51 \* s) - (24 \* (21 + (7 \* s))) = 14 \* 18
(51 \* s) - (453 + (168 \* s)) = 252

Combine like terms:

-117 \* s = -252 + 453
-117 \* s = 191

Divide both sides by -117:

s = 191 / -117
s = -1 \* (191 / 117)
s = -1 \* (63 + 55 / 117)
s = -1 \* (63 + 1 / 2)
s = -63 - 1 / 2
s = -63.5

Now, substitute this value of s into the expression for p:

p = (21 + (7 \* -63.5)) / 18
p = (21 - 445) / 18
p = -424 / 18
p = -23 / 1
p = -23

So, the values of p and s that satisfy both equations are p = -23 and s = -63.5.
### Answer: p = -23, s = -63.5

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 8x7B:

 To solve the system of equations, we can first multiply the first equation by 11/59 and the second equation by 34/11 to make the coefficients of c the same in both equations:

11/59 * (59c - 34w = 84) becomes c - 3.4w = 9.24
34/11 * (11c + 42w = 98) becomes c + 12.6w = 29.4

Now, subtract the first equation from the second to eliminate c:

(c + 12.6w) - (c - 3.4w) = 29.4 - 9.24
16w = 20.16
w = 20.16 / 16 = 1.26

Substitute w = 1.26 into the first equation to solve for c:

59c - 34(1.26) = 84
59c = 84 + 34(1.26)
59c = 104.64
c = 104.64 / 59 = 1.773228346456693

So, c ≈ 1.77 and w ≈ 1.26.
### Answer: c ≈ 1.77, w ≈ 1.26

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 8x7B:

 To solve the system of equations, we can first add the two equations to eliminate the term with $f$:

$45f + 42z = 101$
$60z - 42f = 13$

Adding the two equations gives:

$18z = 114$

Dividing both sides by 18 gives:

$z = 114 / 18 = 6.33333333333$

Now we can substitute this value of $z$ into the first equation to solve for $f$:

$45f + 42(6.33333333333) = 101$

$45f + 266.666666667 = 101$

Subtracting 266.666666667 from both sides gives:

$45f = -165.666666667$

Dividing both sides by 45 gives:

$f = -165.666666667 / 45 = -3.68113207547$

### Answer: The values of f and z that satisfy the system of equations are approximately -3.6811 and 6.3333, respectively.

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 8x7B:

 To solve for p and u, we can first multiply the first equation by 58/21 to eliminate p when we add the two equations together. This gives us:

(26/21)\*(26*p - 21*u) = 6\*(58/21)
13*p - 7*u = 12\*3
13*p - 7*u = 36

Adding this to the second equation, we get:

(13*p - 7*u) + (15*p + 58*u) = 36 + 83
28*p + 51*u = 119

Now, we can divide the entire equation by 19 to solve for p:

(28*p + 51*u)/19 = 119/19
p + (51/19)*u = 6.263157894736842

We can then solve for u by using the first equation:

26*p - 21*u = 6
26\*(6.263157894736842 - (51/19)*u) - 21*u = 6

Solving this equation for u, we get:

u = -0.02247191011235955

Substituting this value back into the equation for p, we get:

p + (51/19)*(-0.02247191011235955) = 6.263157894736842
p = 6.263157894736842 + 0.618479591836736
p = 6.881637486573578

### Answer: p = 6.881637486573578, u = -0.02247191011235955

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 8x7B:

 To solve for the values of n and s, we can use the substitution or elimination method. Here, I will use the elimination method.
First, let's multiply the first equation by 8 and the second equation by 38 to make the coefficients of s the same in both equations:

1) 92 \* n - 38 \* s = 62
2) 59 \* n + 8 \* s = 75

Multiplying the first equation by 8 gives:
92 \* n - 38 \* s = 62 \* 8
736 \* n - 304 \* s = 496

Multiplying the second equation by 38 gives:
59 \* n + 8 \* s = 75 \* 38
2222 \* n + 304 \* s = 2850

Now, let's add the two equations:
(736 \* n - 304 \* s) + (2222 \* n + 304 \* s) = 496 + 2850
2958 \* n = 3346

Now, let's solve for n:
n = 3346 / 2958
n = 1.131

Now, let's substitute n = 1.131 into the first equation:
92 \* 1.131 - 38 \* s = 62
103.872 - 38 \* s = 62

Now, let's solve for s:
-38 \* s = 62 - 103.872
-38 \* s = -41.872
s = 41.872 / -38
s = -1.102

So, the solution to the system of equations is n = 1.131 and s = -1.102.
### Answer: n = 1.131, s = -1.102

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 8x7B:

 We can solve this system of equations by elimination. First, multiply the first equation by 58/

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 8x7B:

 To solve this system of simultaneous linear equations, we can use the elimination method. First, we'll multiply the first equation by 3 and the second equation by 4 to make the coefficients of h the same in both equations:

(33 * t) + (132 * h) = 330
(392 * t) - (144 * h) = 72

Now, we'll add the two equations to eliminate h:

(33 * t) + (132 * h) + (392 * t) - (144 * h) = 330 + 72
(425 * t) = 402

Next, we'll divide both sides by 425 to find the value of t:

t = 402 / 425 = 1.8867924528301887

Now, we'll substitute the value of t back into the first equation to find the value of h:

(11 * 1.8867924528301887) + (44 * h) = 110
20.75471703113206 + 44 * h = 110

Subtracting 20.75471703113206 from both sides:

44 * h = 89.24528296886794

Finally, divide both sides by 44 to find the value of h:

h = 89.24528296886794 / 44 = 2.028256515656085

### Answer: h = 2.028256515656085, t = 1.8867924528301887

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 8x7B:

 To solve this system of linear equations, we first need to eliminate one of the variables. We can do this by multiplying the first equation by 18 and the second equation by 50, so that the coefficients of $b$ in both equations are equal:

$18((69b)-(50o))=18(55)$

$50((41o)+(18b))=50(85)$

This gives us:

$1143b-900o=990$

$2050o+990b=4250$

Next, we can add these two equations to eliminate $o$:

$1143b+990b=990+4250$

$2133b=5240$

Now, we can solve for $b$:

$b=5240/2133$

$b=2.456$

Finally, we can substitute this value of $b$ into either equation to solve for $o$. We'll use the first equation:

$((69*2.456)-(50o))=55$

$168.48-50o=55$

$50o=113.48$

$o=113.48/50$

$o=2.27$

### Answer: b = 2.456 and o = 2.27

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 8x7B:

 To solve the system of equations, we first multiply the second equation by 16 to eliminate the variable p in the first equation:

6 * q + 5 * p = 177 \* 16 = 2832

Now, we have:

67 * q - 80 * p = 65
6 * q + 5 * p = 2832

Adding both equations, we get:

67 * q - 80 * p + 6 * q + 5 * p = 65 + 2832

Simplifying, we get:

73 * q - 75 * p = 2997

Now, we can multiply the second equation by 15 to eliminate the variable p in the new equation:

6 * q + 5 * p = 177 \* 15 = 2655

Now, we have:

73 * q - 75 * p = 2997
6 * q + 5 * p = 2655

Adding both equations, we get:

79 * q = 5652

Dividing by 79, we get:

q = 5652 / 79
q = 71.42

Now, we can substitute the value of q in the second equation to find the value of p:

6 * 71.42 + 5 * p = 2655

Simplifying, we get:

428.52 + 5 * p = 2655

Subtracting 428.52 from both sides, we get:

5 * p = 2226.48

Dividing by 5, we get:

p = 2226.48 / 5
p = 445.296

So, the values of p and q are approximately 445.296 and 71.42, respectively.

### Answer: p ≈ 445.296, q ≈ 71.42

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 8x7B:

 To solve for k and f, we can first multiply the second equation by 4 to make the coefficients of f the same in both equations:

33k - 41f = 31
132k - 164f = 124

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

(10k + 48f) + (132k - 164f) = 161 + 124
142k - 116f = 285

Now, we can solve for k:

k = (285 + 116f) / 142

Now, we can substitute this expression for k into the first equation:

10((285 + 116f) / 142) + 48f = 161

Solving for f:

f = 2

Now, we can substitute f = 2 into the expression for k:

k = (285 + 116*2) / 142
k = 3

So, the values of k and f that satisfy the system of equations are k = 3 and f = 2.
### Answer: k = 3, f = 2

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 8x7B:

 To solve the system of equations, we first need to isolate one of the variables in one of the equations. In the second equation, if we isolate n, we get:

n = 103 - 73*l

Now, we can substitute this expression for n into the first equation:

31 = 58*l - (103 - 73*l)

Simplifying, we get:

31 = 131*l - 103

Adding 103 to both sides, we get:

134 = 131*l

Dividing both sides by 131, we get:

l = 134 / 131 = 1.023

Now, we can substitute this value of l back into the equation for n:

n = 103 - 73*1.023 = 103 - 74.799 = 28.201

Since l and n must be integers, we can round l to 1 and n to 28.

### Answer: l = 1, n = 28

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 8x7B:

 To solve for y and j, we can first isolate one of the variables in one of the equations and then substitute that expression into the other equation.

Let's isolate y in the first equation:
29y = 39 + 28j
y = (39 + 28j) / 29

Now, substitute this expression for y into the second equation:
25((39 + 28j) / 29) + 37j = 116

Solving for j:
(3510 + 2030j) / 29 + 37j = 116 \* 29
3510 + 2030j + 1033j = 33040
2030 + 1033j = 33040 / 3
2030 + 1033j = 11013
1033j = 11013 - 2030
1033j = 8983
j = 8983 / 1033
j = 8.71 (approximately)

Now, substitute this value of j back into the expression for y:
y = (39 + 28 \* 8.71) / 29
y = (39 + 244.08) / 29
y = 283.08 / 29
y = 9.76 (approximately)

Therefore, the values of y and j that satisfy the given system of equations are approximately y = 9.76 and j = 8.71.
### Answer: y ≈ 9.76, j ≈ 8.71

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 8x7B:

 To solve for u and a, we can use the substitution or elimination method. Here, I will use the elimination method.
First, let's multiply the first equation by 2 and the second equation by 1 so that the a-terms can be eliminated:

1. 93u - 85a = 74 \* 2 => 186u - 170a = 148
2. 96u + 17a = 186 \* 1 => 96u + 17a = 186

Now, let's add the two equations:

(186u - 170a) + (96u + 17a) = 148 + 186

This simplifies to:

282u = 334

Now, let's solve for u:

u = 334 / 282

u = 1.1844

Now, let's substitute u = 1.1844 into the first equation to solve for a:

93(1.1844) - 85a = 74

108.2272 - 85a = 74

Now, let's solve for a:

85a = 108.2272 - 74

85a = 34.2272

a = 34.2272 / 85

a = 0.4027

### Answer: u = 1.1844, a = 0.4027

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 8x7B:

 To solve for u and g, we can first multiply the first equation by 23 and the second equation by 61, so that the coefficients of g in both equations are equal:

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

This gives us:

2231*u - 1423*g = 345
5135*u + 1383*g = 11506

Adding these two equations together, we get:

7366*u + -50*g = 11851

Dividing by 50, we get:

147.32*u - g = 237.02

Rounding u to two decimal places, we get:

u = (237.02 + g) / 147.32

Substituting this expression for u into the first equation, we get:

97*(237.02 + g) / 147.32 - 61*g = 15

Solving for g, we get:

g = 1.98

Substituting this value for g into the expression for u, we get:

u = (237.02 + 1.98) / 147.32

u = 1.61

Therefore, the solution to the pair of simultaneous equations is:

u = 1.61
g = 1.98
### Answer: u = 1.61, g = 1.98

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 8x7B:

 To find the values of r and b, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 85 and the second equation by 17 to make the coefficients of b the same in both equations:

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

Multiplying the first equation by 85:

17 * 85 * r + 67 * 85 * b = 103 * 85

Multiplying the second equation by 17:

85 * 17 * r + 67 * 17 * b = 187 * 17

Now, we have:

1445 * r + 1149 * b = 8535
1445 * r + 1149 * b = 3179

Subtracting the second equation from the first:

0 * r + 0 * b = 5356

Since the result is a false statement, it means that there is no unique solution for r and b. However, we can find a particular solution by using one of the original equations. Let's use the first equation:

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

We can express r in terms of b:

r = (103 - 67 * b) / 17

Now, we can find a solution for b by trying different integer values and checking if r is an integer. For example, if we try b = 1, we get:

r = (103 - 67 * 1) / 17
r = (103 - 67) / 17
r = 36 / 17
r = 2.1176

Since r is not an integer, b = 1 is not a solution. If we try b = 2, we get:

r = (103 - 67 * 2) / 17
r = (103 - 134) / 17
r = -31 / 17
r = -1.8235

Again, r is not an integer, so b = 2 is not a solution. If we try b = 3, we get:

r = (103 - 67 * 3) / 17
r = (103 - 201) / 17
r = -98 / 17
r = -5.7647

Since r is not an integer, b = 3 is not a solution. If we try b = 4, we get:

r = (103 - 67 * 4) / 17
r = (103 - 268) / 17
r = -165 / 17
r = -9.7059

Since r is not an integer, b = 4 is not a solution. If we try b = 5, we get:

r = (103 - 67 * 5) / 17
r = (103 - 335) / 17
r = -232 / 17
r = -13.6471

Since r is not an integer, b = 5 is not a solution. If we try b = 6, we get:

r = (103 - 67 * 6) / 17
r = (103 - 402) / 17
r = -299 / 17
r = -17.5882

Since r is not an integer, b = 6 is not a solution. If we try b = 7, we get:

r = (103 - 67 * 7) / 17
r = (103 - 469) / 17
r = -366 / 17
r = -21.5294

Since r is not an integer, b = 7 is not a

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 8x7B:

 To solve for the values of t and n, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 2 and the second equation by 3 to make the coefficients of t and n the same in both equations:

1. (170 * n) - (108 * t) = 82
2. (114 * t) + (90 * n) = 378

Now, let's add both equations:

(170 * n) + (90 * n) - (108 * t) + (114 * t) = 82 + 378

Simplify:

260n + 6t = 460

Divide both sides by 6 to isolate t:

t = (460 - 260n) / 6

Now, let's substitute this expression for t into the first equation:

(85 * n) - (54 * (460 - 260n) / 6) = 41

Simplify:

85n - 43(460 - 260n) / 3 = 41

Multiply both sides by 3 to eliminate the fraction:

255n - 43(460 - 260n) = 123

Simplify:

255n - 19830 + 11180n = 123

Combine like terms:

13730n = 19953

Divide both sides by 13730 to isolate n:

n = 19953 / 13730

Simplify:

n = 1.452

Since n is not a whole number, let's try the other value of t:

t = (460 - 260(1.452)) / 6

Simplify:

t = (460 - 377.12) / 6

Simplify:

t = 82.88 / 6

Simplify:

t = 13.81333333333

Since t is not a whole number, there is no solution for this system of equations.
### Answer: No solution (no whole number values for t and n)

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 8x7B:

 We have the following system of equations:

1) 75u - 69q = 5
2) 48u + 25q = 140

To solve for u and q, we can first multiply equation (1) by 25 and equation (2) by 75 to eliminate q:

1) 1875u - 1725q = 125
2) 3600u + 1875q = 10500

Adding these two equations together, we get:
5475u = 10625

Dividing both sides by 5475, we get:
u = 2

Substituting u = 2 into equation (1), we get:
75(2) - 69q = 5
150 - 69q = 5
-69q = -145
q = 145/69
q = 5/3

So, the solution to the system of equations is u = 2 and q = 5/3.
### Answer: u = 2, q = 5/3

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 8x7B:

 To solve for the values of v and x, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 49 and the second equation by 17 to make the coefficients of v the same in both equations:

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

This simplifies to:

(980 * v) + (833 * x) = 7251
(408 * x) - (793 * v) = 306

Next, let's add these two equations:

(980 * v) + (833 * x) + (408 * x) - (793 * v) = 7251 + 306

This simplifies to:

(-83 * v) + (1241 * x) = 7557

Now, let's divide the entire equation by -83 to solve for v:

v = (-1241 * x) / -83
v = (1241 * x) / 83

Now, let's find the value of x that makes v a whole number. We can do this by dividing 83 by 1241 and finding the closest whole number.

83 / 1241 ≈ 0.066667

The closest whole number is 0, so x = 0.

Substituting x = 0 into the equation for v:

v = (1241 * 0) / 83
v = 0

So, the values of v and x are 0 and 0, respectively.
### Answer: v = 0, x = 0

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 8x7B:

 To solve the system of equations, we can first add the two equations together to eliminate the variable g:

(39 \* t + 41 \* g) + (94 \* t - 91 \* g) = 147 + 42
39 \* t + 41 \* g + 94 \* t - 91 \* g = 189
133 \* t - 50 \* g = 189

Next, we can solve for t:

133 \* t = 189 + 50 \* g
t = (189 + 50 \* g) / 133

Now, we can substitute this expression for t into one of the original equations to solve for g. We'll use the first equation:

39 \* t + 41 \* g = 147
39 \* ((189 + 50 \* g) / 133) + 41 \* g = 147

Multiplying both sides by 133 to eliminate the fraction, we get:

39 \* (189 + 50 \* g) + 41 \* g \* 133 = 147 \* 133
7021 + 1950 \* g + 5383 \* g = 19361
7333 \* g = 12340
g = 12340 / 7333
g = 1.68

Substituting this value of g into the expression for t, we get:

t = (189 + 50 \* g) / 133
t = (189 + 50 \* 1.68) / 133
t = (189 + 84) / 133
t = 273 / 133
t = 2.05

Therefore, the solution to the system of equations is t = 2.05 and g = 1.68.
### Answer: t = 2.05, g = 1.68

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 8x7B:

 To solve for the values of c and o, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 55 and the second equation by 6, so that the coefficients of o in both equations are equal:

6c * 55 + 55o * 55 = 112 * 55
55c * 6 - 48o * 6 = 36 * 6

This gives us:

330c + 3025o = 6160
330c - 288o = 216

Now, let's add these two equations:

330c + 3025o + 330c - 288o = 6160 + 216
660c + 2737o = 6376

Next, let's divide both sides by 11:

660c/11 + 2737o/11 = 6376/11
60c + 249o = 579.64

Now, let's multiply the first equation by 249 and the second equation by 60, so that the coefficients of c in both equations are equal:

6c * 249 + 55o * 249 = 112 * 249
55c * 60 - 48o * 60 = 36 * 60

This gives us:

1494c + 13605o = 27966
3300c - 2880o = 2160

Now, let's add these two equations:

1494c + 13605o + 3300c - 2880o = 27966 + 2160
4794c + 10725o = 30126

Now, let's divide both sides by 4794:

c + 2235o/4794 = 30126/4794
c = 30126/4794 - 2235o/4794

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

6(30126/4794 - 2235o/4794) + 55o = 112
180756/4794 - 13410o/4794 + 55o = 112

Now, let's multiply both sides by 4794:

180756 + 4794(-13410o/4794 + 55o) = 112 * 4794
180756 + (-611220o + 260570o) = 535296

This gives us:

-350650o = -354540

Now, let's divide both sides by -350650:

o = -354540 / -350650
o = 1.011

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

c = 30126/4794 - 2235 * 1.011 / 4794
c = 30126/4794 - 2261.515 / 4794
c = 27864.485 / 4794
c = 5.81

Since c must be a whole number, we can round c to the nearest whole number, which is 6.

Therefore, the values of c and o that satisfy the given system of equations are c = 6 and o = 1.011 (rounded to two decimal places).

### Answer

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 8x7B:

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

First, let's multiply the first equation by 71 and the second equation by 8:

8w*71 + 68u*71 = 170*71
71w*8 - 94u*8 = 8*8

This gives us:
568w + 4808u = 1207
568w - 752u = 64

Now, let's add the two equations:

568w + 4808u + 568w - 752u = 1207 + 64
1136w + 4056u = 1271

Next, divide both sides by 4:

1136w/4 + 4056u/4 = 1271/4
284w + 1014u = 317.75

Now, let's multiply the first equation by 1014 and the second equation by 284:

8w*1014 + 68u*1014 = 170*1014
19536w - 26552u = 170*284

This gives us:
80992w + 690432u = 17218
19536w - 26552u = 48896

Now, let's add the two equations:

80992w + 690432u + 19536w - 26552u = 17218 + 48896
99028w + 663880u = 66114

Next, divide both sides by 19806:

99028w/19806 + 663880u/19806 = 66114/19806
5w + 335u = 33.333333333333336

Now, let's multiply the first equation by 335 and the second equation by 5:

8w*335 + 68u*335 = 170*335
3575w - 470u = 1675

This gives us:
2680w + 22760u = 5695
3575w - 470u = 1675

Now, let's add the two equations:

2680w + 22760u + 3575w - 470u = 5695 + 1675
6255w + 22290u = 7370

Next, divide both sides by 315:

6255w/315 + 22290u/315 = 7370/315
20w + 70.76335877862596u = 23.43614457831325

Now, let's multiply the first equation by 70.76335877862596 and the second equation by 20:

8w*70.76335877862596 + 68u*70.76335877862596 = 170*70.76335877862596
71w*20 - 94u*20 = 8*20

This gives us:
568w + 4808u = 1207.0000000000002
142

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 8x7B:

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

First, let's multiply the first equation by 38 and the second equation by 8:

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

This gives us:

2584*r + 304*f = 3496
776*f + 304*r = 1456

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

2584*r - 776*f = 3496 - 1456
2584*r - 776*f = 2040

Divide the entire equation by 4:

646*r - 194*f = 510

Now, let's multiply the second equation by 3:

776*f*3 + 304*r*3 = 1456*3
2328*f + 912*r = 4368

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

2328*f - (646*r - 194*f) = 4368 - 510
2328*f - 646*r + 194*f = 3858
2134*f - 646*r = 3858

Divide the entire equation by 2:

1067*f - 323*r = 1929

Now, let's multiply the first equation by 323 and the second equation by 1067:

646*r*323 + 8*f*323 = 92*323
1067*f*1067 - 323*r*1067 = 1929*1067

This gives us:

209958*r + 2664*f = 30009
1146849*f - 344466*r = 2054863

Now, let's add the first equation to the second:

209958*r + 2664*f + 1146849*f - 344466*r = 30009 + 2054863
-134508*r + 1149513*f = 2084872

Divide the entire equation by -1:

134508*r - 1149513*f = -2084872

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

(134508*r - 1149513*f) - (1067*f - 323*r) = -2084872 - 1929
134185*r - 1146246*f = -2086801

Divide the entire equation by 13:

10321.92*r - 88172.8*f = -160523.15

Now, let's multiply the first equation by 88172.8 and the second equation by 10321.92:

10321.92*r*88172.8 - 88172.8*f*88172.8 = -160523.15*88172.8
10321.92*r*10321.92 - 1146246*f*10321.92 =

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 8x7B:

 To find the values of d and r, we can first solve one equation for one variable and then substitute that expression into the other equation.

Let's solve the first equation for d:
67d - 37r = 50
67d = 50 + 37r
d = (50 + 37r) / 67

Now, substitute this expression for d into the second equation:
39r - 21( (50 + 37r) / 67) = 16

Solving for r, we get:
r = 16/39 \* 67 / (1 - 21/67)
r = 16/39 \* 67 / (46/67)
r = 16 \* 67 / 46
r = 16 \* 1.4565
r = 23.26 (rounded to two decimal places)

Now, substitute the value of r into the expression for d:
d = (50 + 37\*23.26) / 67
d = (50 + 857.02) / 67
d = 907.02 / 67
d = 13.54 (rounded to two decimal places)

So, the cost of each apple is $13.54 and the cost of each ragdoll is $23.26.
### Answer: d = $13.54, r = $23.26

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 8x7B:

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

First, let's multiply the first equation by 98 and the second equation by 50 to make the coefficients of x the same in both equations:

First equation: 163 \* 98 = 50x \* 98 + a \* 98 => 15854 = 4900x + 98a
Second equation: 24 \* 50 = 98x \* 50 - 84 \* 50a => 1200 = 4900x - 4200a

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

15854 - 1200 = (4900x + 98a) - (4900x - 4200a) => 14654 = 98a + 4200a

Combine like terms:

14654 = 5298a

Now, divide both sides by 5298:

a = 14654 / 5298
a = 2.77 (rounded to two decimal places)

Now, substitute a = 2.77 into the first equation:

163 = 50x + 2.77

Subtract 2.77 from both sides:

160.23 = 50x

Divide both sides by 50:

x = 160.23 / 50
x = 3.20 (rounded to two decimal places)

### Answer: x approximately equals 3.20 and a approximately equals 2.77.

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 8x7B:

 To solve the system of equations, we can first multiply the first equation by 2 and the second equation by 3 to eliminate the variable $b$ in the second equation and the variable $p$ in the first equation. This will give us:

$2 \times (67p + 18b) = 2 \times 110$
$3 \times (82b - 44p) = 3 \times 58$

Simplifying, we get:

$134p + 36b = 220$
$246b - 132p = 174$

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

$(134p + 36b) + (246b - 132p) = 220 + 174$

Simplifying, we get:

$282b = 394$

Dividing both sides by 282, we get:

$b = \frac{394}{282} = \frac{197}{141}$

Now, we can substitute this value of $b$ into either of the original equations to find the value of $p$. We'll use the first equation:

$67p + 18 \times \frac{197}{141} = 110$

Simplifying, we get:

$67p = 110 - \frac{354}{141} = \frac{15420 - 354}{141} = \frac{15066}{141}$

Dividing both sides by 67, we get:

$p = \frac{15066}{141 \times 67} = \frac{15066}{9407}$

Therefore, the solution to the system of equations is:

### Answer: p = 15066/9407 and b = 197/141.

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 8x7B:

 We can write the two equations as follows:
1) 63c - 36e = 27
2) 8c + 32e = 69

First, we can solve the second equation for e:
e = (69 - 8c) / 32

Now, substitute this expression for e into the first equation:
63c - 36((69 - 8c) / 32) = 27

Solving this equation for c, we get:
c = 2

Now, substitute c = 2 into the equation for e:
e = (69 - 8*2) / 32
e = 7/8

So, the solution is c = 2 and e = 7/8.
### Answer: c = 2, e = 7/8

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 8x7B:

 To solve the system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 51 and the second equation by 29, so that when we add the two equations together, the p terms will cancel out:

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

This gives us:

1356*x + 1479*p = 5487
1779*x - 1479*p = 116

Adding these two equations together, we get:

3135*x = 5603

Dividing both sides by 3135, we find:

x = 5603 / 3135
x = 1.818

Now, we can substitute this value of x into either of the original equations to find the value of p. We'll use the first equation:

26*1.818 + 29*p = 107

Solving for p, we get:

29*p = 107 - 26*1.818
29*p = 107 - 47.728
29*p = 59.272
p = 59.272 / 29
p = 2.044

So, the solution to the system of linear equations is x = 1.818 and p = 2.044.
### Answer: x = 1.818, p = 2.044

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 8x7B:

 To solve for g and l, we can first isolate one variable in one of the equations and then substitute that expression into the other equation to solve for the other variable.

Let's isolate l in the first equation:

(29 \* l) + (17 \* g) = 68
(29 \* l) = 68 - (17 \* g)
l = (68 - (17 \* g)) / 29

Now, we can substitute this expression for l into the second equation:

(31 \* g) - (10 \* ((68 - (17 \* g)) / 29)) = 17

Solving this equation for g, we get:

g = 1

Now, we can substitute g = 1 into the expression for l:

l = (68 - (17 \* 1)) / 29
l = 3

So, the solution to the system of equations is g = 1 and l = 3.
### Answer: g = 1, l = 3

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 8x7B:

 To find the values for a and c, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 2 and the second equation by 3:

66\*a - 108\*c = 60

72\*a - 78\*c = 87

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

(66\*a - 108\*c) - (72\*a - 78\*c) = 60 - 87

-6\*a + 30\*c = -27

Now, let's divide both sides by -6:

a - 5\*c = -4.5

Since a and c are integers, there is no solution for this system of equations.
### Answer: There is no solution for a and c.

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 8x7B:

 Reasoning: We can solve this system of equations by using the elimination method. First, we'll multiply the first equation by 84 and the second equation by 71 to eliminate the variable d.

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

Now, we'll add the two equations:

(71 * 84 * d + 84 * 9 * j) + (71 * 43 * j - 71 * 84 * d) = (132 * 84) + (91 * 71)
(71 * 84 * d - 71 * 84 * d) + (84 * 9 * j + 71 * 43 * j) = 11172 + 6491
0 + 1203 * j = 17663

Now, we'll solve for j:

1203 * j = 17663
j = 17663 / 1203
j = 14.68 (rounded to two decimal places)

Now, we'll substitute j = 14.68 into the first equation:

71 * d + 9 * 14.68 = 132
71 * d = 132 - 132.12
71 * d = -0.12
d = -0.12 / 71
d = -0.0017 (rounded to three decimal places)

### Answer: d = -0.0017, j = 14.68 (rounded to two decimal places)

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 8x7B:

 To solve this system of equations, we can first isolate one variable in one of the equations and then substitute that expression into the other equation to solve for the other variable.

Let's isolate o in the first equation:

81o + 26n = 163
81o = 163 - 26n
o = (163 - 26n) / 81

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

87n + 23((163 - 26n) / 81) = 143

To solve for n, first multiply both sides by 81 to eliminate the fraction:

87n \* 81 + 23(163 - 26n) = 143 \* 81
7057n + 3719 - 608n = 11533

Combine like terms:

6449n = 7814

Divide both sides by 6449 to solve for n:

n = 7814 / 6449
n = 1.212

Since n must be a whole number, we can round n to the nearest whole number, which is 1. Substitute n = 1 into the expression for o:

o = (163 - 26n) / 81
o = (163 - 26 \* 1) / 81
o = (163 - 26) / 81
o = 137 / 81
o = 1.691

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

Therefore, the values of o and n that satisfy the system of equations are o = 2 and n = 1.
### Answer: o = 2, n = 1

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 8x7B:

 To solve the system of equations, we can first multiply the first equation by 67 and the second equation by 61, so that the coefficients of $w$ in both equations are the same:

$46 \times 67 \times s - 61 \times 67 \times w = 2 \times 67$

$61 \times 61 \times s + 67 \times 61 \times w = 178 \times 61$

This gives us:

$3092 \times s - 4087 \times w = 139$

$3721 \times s + 4087 \times w = 10818$

Adding these two equations, we get:

$6813 \times s = 11957$

So, $s = 11957 / 6813 = 1.7559...$

Substituting this value of $s$ into the first equation, we get:

$46 \times 1.7559... \times s - 61 \times w = 2$

$81.59... \times s - 61 \times w = 2$

$81.59... \times 1.7559... - 61 \times w = 2$

$142.17... - 61 \times w = 2$

$61 \times w = 140.17...$

$w = 140.17... / 61 = 2.3011...$

So, the solution to the system of equations is $s = 1.7559...$ and $w = 2.3011...$

### Answer: $s = 1.7559...$ and $w = 2.3011...$ (rounded to 5 decimal places)

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 8x7B:

 To solve for i and k, we can first multiply the first equation by 3 and the second equation by 5, so that the coefficients of i and k are the same in both equations:

51*k - 8*i = 86 becomes 153*k - 24*i = 258
39*i + 8*k = 193 becomes 195*i + 40*k = 965

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

195*i + 40*k - 153*k + 24*i = 965 - 258
219*i = 707

Now, we can solve for i:

i = 707 / 219
i = 3.2324

Now, we can substitute i = 3.2324 into the first equation to solve for k:

51*k - 8*3.2324 = 86
51*k = 86 + 25.8592
51*k = 111.8592
k = 111.8592 / 51
k = 2.1937

### Answer: i = 3.2324, k = 2.1937

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 8x7B:

 To solve the system of equations, we first need to isolate one of the variables in the second equation. We can solve for l:

l = 126 - 93m

Now, substitute this expression for l into the first equation:

26m + 17(126 - 93m) = 146

Now, simplify and solve for m:

26m + 2118 - 1511m = 146
-1485m = -1972
m = -1972 / -1485
m = 1.327 (approximately)

Now, substitute this value of m back into the equation for l:

l = 126 - 93(1.327)
l = 126 - 122.451
l = 3.549 (approximately)

Since the values of m and l are approximations, we can round them to two decimal places:

m = 1.33 (approximately)
l = 3.55 (approximately)

### Answer: l ≈ 3.55, m ≈ 1.33

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 8x7B:

 To solve for 'f' and 'h' in this system of equations, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 29 and the second equation by 8 to make the coefficients of 'f' the same in both equations:

1) (29 * 8 * f) + (29 * 39 * h) = (29 * 66)
2) (8 * 29 * f) + (8 * 46 * h) = (8 * 119)

This gives us:

1) 232 * f + 1131 * h = 1974
2) 232 * f + 368 * h = 952

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

(232 * f - 232 * f) + (1131 * h - 368 * h) = (1974 - 952)
763 * h = 1022

Now, divide both sides by 763 to solve for 'h':

h = 1022 / 763
h = 1.3378 (rounded to four decimal places)

Now, let's substitute 'h' back into either equation to solve for 'f'. We'll use the first equation:

(8 * f) + (39 * 1.3378) = 66
8 * f = 66 - 52.0526
8 * f = 13.9474

Now, divide both sides by 8 to solve for 'f':

f = 13.9474 / 8
f = 1.7434 (rounded to four decimal places)

### Answer: h ≈ 1.3378 and f ≈ 1.7434

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 8x7B:

 To solve for k and b, we can first isolate one variable in one of the equations. I will isolate b in the first equation:

22 * b = 109 - 23 * k
b = (109 - 23 * k) / 22

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

62 * k - 69 * (109 - 23 * k) / 22 = 14

To solve for k, first multiply both sides by 22:

62 * 22 * k - 69 * (109 - 23 * k) = 14 \* 22

Expand and simplify:

1364 * k - 7509 + 1597 * k = 308

2961 * k = 3307

k = 3307 / 2961

k = 1.1162

Now, substitute this value of k back into the expression for b:

b = (109 - 23 * 1.1162) / 22

b = (109 - 25.677) / 22

b = 83.323 / 22

b = 3.7874

Since k and b are not integers, we can conclude that there are no integer values of k and b that satisfy the given system of equations.

### Answer: There are no integer values of k and b that satisfy the given system of equations.

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 8x7B:

 To solve the system of linear equations for the values of m and s, we can use the substitution or elimination method. Here, I will use the elimination method.

First, let's multiply the first equation by 2 and the second equation by 55 to eliminate the s variable:

1. 168m - 110s = 2
2. 3465m - 110s = 5410

Now, subtract the second equation from the first:

(168m - 110s) - (3465m - 110s) = 2 - 5410
-3297m = -5408

Now, divide both sides by -3297:

m = -5408 / -3297
m = 1.64

Now, substitute the value of m into the first equation:

84(1.64) - 55s = 1
136.96 - 55s = 1

Now, subtract 136.96 from both sides:

-55s = -135.96

Now, divide both sides by -55:

s = -135.96 / -55
s = 2.47

So, the values of m and s are approximately 1.64 and 2.47, respectively.

### Answer: m ≈ 1.64, s ≈ 2.47.

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 8x7B:

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

First, let's multiply the first equation by 95 and the second equation by 6 to make the coefficients of b the same in both equations:

1. (6 * b) * 95 + (5 * k) * 95 = 105 * 95
95(6b + 5k) = 9975
570b + 475k = 9975

2. (95 * k) * 6 - (51 * b) * 6 = 67 * 6
6(95k - 51b) = 402
570b + 475k = 9975

Now, we can eliminate the term with b by subtracting the second equation from the first:

(570b - 570b) + (475k - 474k) = 9975 - 402
k = 9573 / 474
k = 20.173

Now, we can substitute k into the first equation to find b:

(6 * b) + (5 * 20.173) = 105
6b = 105 - 100.865
6b = 4.135
b = 4.135 / 6
b = 0.689

So, the values of b and k are approximately 0.689 and 20.173, respectively.

### Answer: b ≈ 0.689, k ≈ 20.173

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 8x7B:

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

First, let's multiply the first equation by 4 and the second equation by 62 to make the coefficients of d the same in both equations:

4(33d + 62u) = 4(114)
62(32u + 40d) = 62(83)

This gives us:

132d + 248u = 456
1984u + 2496d = 5146

Next, let's subtract the first equation from the second equation:

(1984u + 2496d) - (132d + 248u) = 5146 - 456

This simplifies to:

1852u + 2264d - 132d - 248u = 4690

Combining like terms, we get:

1604u + 2022d = 4690

Dividing the entire equation by 2, we get:

802u + 1011d = 2345

Now, let's multiply the first equation by 1011 and the second equation by 802 to make the coefficients of u the same in both equations:

1011(33d + 62u) = 1011(114)
802(40d + 32u) = 802(83)

This gives us:

33343d + 62826u = 115294
32080d + 25664u = 66086

Next, let's subtract the second equation from the first equation:

(33343d + 62826u) - (32080d + 25664u) = 115294 - 66086

This simplifies to:

1263d + 37162u = 49208

Dividing the entire equation by 1263, we get:

d + 29.41u = 38.98

Now, let's substitute d = 38.98 - 29.41u into the first equation:

33(38.98 - 29.41u) + 62u = 114

This simplifies to:

1263.34 - 964.67u + 62u = 114

Combining like terms, we get:

-802.67u = -1149.34

Dividing the entire equation by -802.67, we get:

u = 1.43

Substituting u = 1.43 into the equation d = 38.98 - 29.41u, we get:

d = 38.98 - 29.41(1.43)

This simplifies to:

d = 38.98 - 42.19

Therefore, d = -3.21.

### Answer: d = -3.21 and u = 1.43

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 8x7B:

 To solve this system of equations, we can first multiply the first equation by 4 and the second equation by 1 to make the coefficients of p the same in both equations:

1. 5 * c + 28 * p = 102 (multiply by 4)
2. 80 * c - 268 * p = 13 (multiply by 1)

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

(5 * c + 28 * p) + (80 * c - 268 * p) = 102 + 13
85 * c - 240 * p = 115

Next, we can divide the equation by 5 to solve for c:

c = (115 + 240 * p) / 85

Now, we can substitute c into the first equation to solve for p:

5 * ((115 + 240 * p) / 85) + 28 * p = 102
(575 + 1200 * p) / 85 + 28 * p = 102
575 + 1200 * p = 85 * 102 + 2240 * p
575 - 2240 * p = 8690
-2065 * p = 8115
p = 8115 / -2065
p = -3.93

Now, we can substitute p into the equation for c:

c = (115 + 240 * -3.93) / 85
c = (115 - 943.2) / 85
c = -828.2 / 85
c = -9.74

However, the values of c and p are not whole numbers, which contradicts the assumption that c and p are integers. Therefore, the system of equations has no integer solutions.

### Answer: The system of equations has no integer solutions.

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 8x7B:

 To solve for r and q, we can first isolate one of the variables in one of the equations. In the second equation, we can solve for r in terms of q:

97q - 76r = 76
-76r = 76 - 97q
r = (97q - 76) / -76

Now, we can substitute this expression for r into the first equation:

58r + 12q = 147
58((97q - 76) / -76) + 12q = 147

Simplifying this equation, we get:

-7q + 58 = 147
-7q = 89
q = 89 / -7
q = -12.714285714285714

Now, we can substitute this value of q into the equation for r:

r = (97(-12.714285714285714) - 76) / -76
r = (1223.5 - 76) / -76
r = 1147 / 76
r = 15.092105263157895

### Answer: r ≈ 15.092, q ≈ -12.714

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 8x7B:

 To solve for v and k, we can use the method of elimination. First, we'll eliminate one of the variables by multiplying one or both of the equations so that the coefficients of that variable are equal and opposite.

Let's eliminate the variable k. To do this, we'll multiply the first equation by 2 and the second equation by 3:

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 by dividing both sides of the equation by 313:

v = 404 / 313
v = 1.29

Now, we can substitute this value of v into either of the original equations to solve for k. We'll use the first equation:

47*1.29 - 3*k = 10

Solving for k:

k = (47*1.29 - 10) / 3
k = (60.13 - 10) / 3
k = 50.13 / 3
k = 16.71

So, the solution to the system of equations is v = 1.29 and k = 16.71.

### Answer: v = 1.29, k = 16.71

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 8x7B:

 We can write the system of equations as:
89p - 41q = 60 (Equation 1)
27p + 91q = 124 (Equation 2)

To solve for p and q, we can first multiply Equation 1 by 3 and Equation 2 by 11, so that the coefficients of q in both equations are equal:
267p - 123q = 180 (3 \* Equation 1)
298p + 1001q = 1364 (11 \* Equation 2)

Next, we can subtract the first equation from the second equation:
298p - 267p = 1364 - 180
31p = 1184

Now, we can solve for p:
p = 1184 / 31
p = 38.226 (approximately)

Next, we can substitute p = 38.226 into Equation 1:
89(38.226) - 41q = 60
3392.534 - 41q = 60

Now, we can solve for q:
41q = 3392.534 - 60
41q = 3332.534
q = 3332.534 / 41
q = 81.28 (approximately)

Therefore, the values of p and q are approximately p = 38.226 and q = 81.28.
### Answer: p ≈ 38.226, q ≈ 81.28

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 8x7B:

 To solve this system of equations, we can first multiply the first equation by 3 and the second equation by 2 to make the coefficients of $d$ equal in both equations:

Multiplied first equation: 3((88 * u) - (96 * d)) = 3(12) => 264u - 288d = 36

Multiplied second equation: 2((27 * u) + (36 * d)) = 2(71) => 54u + 72d = 142

Now, we can add both equations to eliminate $d$:

264u - 288d + 54u + 72d = 36 + 142 => 318u = 178

Now, we can find the value of $u$:

u = 178 / 318 = 89 / 159

Now, we can substitute the value of $u$ into the first equation to find the value of $d$:

(88 * (89 / 159)) - (96 * d) = 12 => 88 * 89 / 159 - 96d = 12

Now, we can solve for $d$:

96d = 88 * 89 / 159 - 12 => d = (88 * 89 - 12 * 159) / (96 * 159) = 71 / 159

### Answer: u = 89 / 159 and d = 71 / 159

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 8x7B:

 To solve the system of equations, we can first multiply the second equation by 2 to eliminate the variable f:

2 * (3 \* n - 2 \* f) = 2 \* 70
6 \* n - 4 \* f = 140

Now, we can subtract the first equation multiplied by 2 from the second equation:

(6 \* n - 4 \* f) - 2 \* (20 \* n - 18 \* f) = 140
6 \* n - 4 \* f - 40 \* n + 36 \* f = 140
-34 \* n + 32 \* f = 140

Next, we can divide both sides by -32 to isolate n:

n = -140 / 32
n = -45 / 10
n = -9/2

Now, we can substitute the value of n into the first equation to find the value of f:

20 \* (-9/2) - 18 \* f = 9
-90 - 18 \* f = 9
-18 \* f = 99
f = -99 / 18
f = -11

### Answer: f = -11, n = -9/2

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 8x7B:

 To solve for j and l, we can use 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 the same in both equations:

259*l + 3619*j = 4901
3619*j + 3593*l = 7372

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

(-42)*l = -2471

Dividing both sides by -42, we get:

l = 2471 / 42 = 58.8333...

Since l is a whole number, we can round it to the nearest whole number, which is 59.

Now, let's substitute l = 59 into the first equation:

7*59 + 97*j = 133
393 + 97*j = 133
97*j = 133 - 393
97*j = -260

Dividing both sides by 97, we get:

j = -260 / 97 = -2.6896...

Since j is not a whole number, we made an error in rounding l. Let's try rounding l down to 58 instead:

7*58 + 97*j = 133
406 + 97*j = 133
97*j = 133 - 406
97*j = -273

Dividing both sides by 97, we get:

j = -273 / 97 = -2.8041...

Since j is still not a whole number, we made an error in rounding l. Let's try rounding l up to 60 instead:

7*60 + 97*j = 133
420 + 97*j = 133
97*j = 133 - 420
97*j = -287

Dividing both sides by 97, we get:

j = -287 / 97 = -2.9587...

Since j is still not a whole number, we made an error in rounding l. Let's try solving the equations without rounding l:

7*l + 97*j = 133
22*j + 37*l = 76

Multiplying the first equation by 37 and the second equation by 97, we get:

259*l + 3619*j = 4901
2114*j + 3593*l = 7372

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

(-45)*l = -139

Dividing both sides by -45, we get:

l = 139 / 45 = 3.0888...

Since l is not a whole number, we made an error in our calculations. Let's try solving the equations again, but this time we will use the substitution method.

From the first equation, we can express j in terms of l:

j = (133 - 7*l) / 97

Substituting this expression for j into the second equation, we get:

22*(133 - 7*l) / 97 + 37*l = 76

Multiplying both sides by 97, we get:

22*133 - 22*7*l + 3593*l = 7372

Simplifying, we get:

22*133 + 3571*l = 7372
3571*l = 7372 - 22*133
3571*l = 6947

Dividing both sides by 3571, we

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 8x7B:

 To solve for d and f, we can first multiply the first equation by 4 and the second equation by 3 to eliminate the fraction in the first equation:

84d - 184f = 212
24d + 252f = 399

Now, add the two equations:

84d - 184f + 24d + 252f = 212 + 399
108d + 68f = 611

Divide the entire equation by 4 to solve for d:

d = (611 - 68f) / 108

Now, substitute this expression for d into one of the original equations. We'll use the first equation:

21d - 46f = 53
21((611 - 68f) / 108) - 46f = 53

Multiply both sides by 108 to eliminate the denominator:

21(611 - 68f) - 46f \* 108 = 53 \* 108
12811 - 1378f - 46f \* 108 = 5616

Now, solve for f:

12811 - 1378f - 46f \* 108 = 5616
12811 - 1378f - 4848f = 5616
-6226f = -7195
f = 7195 / -6226
f = -1.156

Now, substitute f = -1.156 into the equation for d:

d = (611 - 68f) / 108
d = (611 - 68 \* -1.156) / 108
d = (611 + 78.45) / 108
d = 689.45 / 108
d = 6.39

So, the solution to the system of equations is d = 6.39 and f = -1.156. However, since d and f represent the number of some unit, they must be integers. Therefore, the system of equations has no solution.

### Answer: The system of equations has no solution.

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 8x7B:

 To solve for u and w, we can first isolate one of the variables in one of the equations. In the second equation, we can isolate u:

66u = 21 + 68w
u = (21 + 68w) / 66

Now, we can substitute this expression for u into the first equation:

74((21 + 68w) / 66) + 11w = 116
(1521 + 4992w) / 66 + 11w = 116

To eliminate the fraction, we can multiply both sides of the equation by 66:

1521 + 4992w + 726w = 7536
4992w + 726w = 7536 - 1521
5718w = 6015

Now, we can solve for w:

w = 6015 / 5718
w = 1.052

Now, we can substitute this value of w back into the equation for u:

u = (21 + 68(1.052)) / 66
u = (21 + 68(1.052)) / 66
u = (21 + 71.536) / 66
u = 92.536 / 66
u = 1.402

Therefore, the values of u and w that satisfy the given system of equations are approximately u = 1.402 and w = 1.052.
### Answer: u ≈ 1.402, w ≈ 1.052

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 8x7B:

 To solve for f and j, we can first isolate one of the variables in one of the equations. I will isolate f in the first equation:

76f - 42j = 96
76f = 96 + 42j
f = (96 + 42j) / 76

Now, substitute this expression for f into the second equation:

47j + 34((96 + 42j) / 76) = 136

To solve for j, first multiply both sides by 76 to eliminate the fraction:

47 \* 76j + 34 \* 96 + 34 \* 42j = 136 \* 76
3592j + 3264 + 1468j = 10336
5060j = 7072
j = 7072 / 5060
j = 1.4 (rounded to one decimal place)

Now, substitute j = 1.4 into the expression for f:

f = (96 + 42 \* 1.4) / 76
f = (96 + 58.8) / 76
f = 154.8 / 76
f = 2.03 (rounded to two decimal places)

Therefore, f ≈ 2.03 and j ≈ 1.4 satisfy the given system of equations.
### Answer: f ≈ 2.03, j ≈ 1.4

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 8x7B:

 To solve this system of equations, we can first add the two equations together to eliminate one of the variables. This will allow us to solve for the other variable.

(68u + 32e) + (63e - 69u) = 174 + 1
68u + 32e + 63e - 69u = 175
-1u + 95e = 175

Now, we can solve for e by dividing both sides of the equation by 95.

-1u + 95e / 95 = 175 / 95
-1u + e = 1.8421 (approximately)

Now, we can solve for u by using the first equation and substituting the value of e we just found.

68u + 32(1.8421) = 174
68u + 58.7072 = 174
68u = 115.2928
u = 115.2928 / 68
u = 1.6958 (approximately)

So, the solution to the system of equations is u ≈ 1.6958 and e ≈ 1.8421.
### Answer: u ≈ 1.6958, e ≈ 1.8421

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 8x7B:

 To find the values of p and n that satisfy the system of linear equations, we can use the elimination method.
First, we'll multiply the first equation by 3 and the second equation by 5 to make the coefficients of n equal in both equations:

57p + 12n = 387
120p + 195n = 770

Now, we'll subtract the first equation from the second equation:

120p - 57p + 195n - 12n = 770 - 387
63p + 183n = 383

Now, we'll divide the entire equation by 3 to get the coefficients of p and n to be integers:

63p/3 + 183n/3 = 383/3
21p + 61n = 127.666666667

Since p and n are integers, this equation has no solution.

However, if we go back to the original system of equations, we can see that the second equation is a multiple of the first equation:

57p + 4n = 129
24p + 39n = 154

Multiplying the first equation by 2 gives us the second equation. Therefore, the system of equations is dependent and has an infinite number of solutions.

### Answer: The system of equations has an infinite number of solutions.

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 8x7B:

 To solve for y and z, we can use the substitution or elimination method. Here, I'll use the elimination method.

First, let's multiply the first equation by 5/11 and the second equation by 22/3 to make the coefficients of z the same in both equations:

(5/11)(66z - 44y) = (5/11)32
(22/3)(60y + 14z) = (22/3)116

This gives us:

30z - 20y = 16
440y + 308z = 856

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

(440y + 308z) - (30z - 20y) = 856 - 16
420y + 278z = 840

Next, let's divide the entire equation by 2:

(420y + 278z)/2 = 840/2
210y + 139z = 420

Now, let's multiply the first equation by 139 and the second equation by 210 to make the coefficients of y the same in both equations:

(139)(210y + 139z) = (139)420
(210)(210y + 139z) = (210)420

This gives us:

29090y + 19181z = 57980
44100y + 29190z = 88200

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

(44100y + 29190z) - (29090y + 19181z) = 88200 - 57980
14910y + 9999z = 30220

Next, let's divide the entire equation by 11:

(14910y + 9999z)/11 = 30220/11
1355y + 909z = 2747

Now, let's multiply the first equation by 9 and the second equation by 5:

(9)(1355y + 909z) = (9)2747
(5)(1355y + 909z) = (5)2747

This gives us:

12195y + 8181z = 24723
6775y + 4545z = 13735

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

(12195y + 8181z) - (6775y + 4545z) = 24723 - 13735
5420y + 3636z = 10988

Next, let's divide the entire equation by 4:

(5420y + 3636z)/4 = 10988/4
1355y + 909z = 2747

Now, let's multiply the first equation by 3 and the second equation by 5:

(3)(1355y + 909z) = (3)2747
(5)(1355y + 909z) = (5)2747

This gives us:

4065y + 2727z = 8241
6775y + 4545z = 13735

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

(4065y + 2727z) - (6775y + 4545z) = 8

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 8x7B:

 To solve the system of equations, we first need to eliminate one of the variables. We can do this by multiplying the first equation by 11 and the second equation by 58, so that the coefficients of t in both equations are equal. This gives us:

83 \* t \* 11 - 58 \* h \* 11 = 45 \* 11
69 \* h \* 58 + 11 \* t \* 58 = 124 \* 58

Simplifying, we get:

913 t - 638 h = 505
4002 h + 638 t = 7272

Adding these two equations, we get:

913 t + 638 t = 505 + 7272
1551 t = 7777

Dividing both sides by 1551, we get:

t = 7777 / 1551
t = 5

Substituting t = 5 in the first equation, we get:

83 \* 5 - 58 \* h = 45
415 - 58 \* h = 45

Subtracting 415 from both sides, we get:

-58 \* h = -370

Dividing both sides by -58, we get:

h = -370 / -58
h = 6.379310344827586

So the solution to the system of equations is t = 5 and h = 6.379310344827586.
### Answer: t = 5, h = 6.379310344827586

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 8x7B:

 To find the values of h and o, we can first notice that both equations are of the form:

(79h - 61o) = 9 and (16h - 12o) = 9

We can simplify both equations by dividing both sides by their respective coefficients of h and o:

79h = 9 + 61o and 16h = 9 + 12o

Now, we can solve for h in the second equation:

h = (9 + 12o) / 16

Substitute this expression for h into the first equation:

79((9 + 12o) / 16) = 9 + 61o

Multiply both sides by 16 to eliminate the fraction:

79(9 + 12o) = 144 + 976o

Expand and simplify:

693 + 948o = 144 + 976o

Subtract 948o from both sides:

-272 = -32o

Divide both sides by -32:

o = 272 / 32 = 8.5

Now, substitute o = 8.5 into the equation h = (9 + 12o) / 16:

h = (9 + 12(8.5)) / 16
h = (9 + 102) / 16
h = 111 / 16
h = 6.9375

Therefore, the values of h and o are approximately 6.9375 and 8.5, respectively.
### Answer: h ≈ 6.9375, o = 8.5

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 8x7B:

 To solve for variables s and y, we can use the substitution or elimination method. Here, I will use the elimination method.
First, let's multiply the first equation by 15 and the second equation by 5, so that the coefficients of s in both equations are equal:

60y + 840s = 2085
325y - 450s = 80

Now, let's add both equations:

(60y + 840s) + (325y - 450s) = 2085 + 80
925y + 390s = 2165

Now, let's solve for y:

925y = 2165 - 390s
y = (2165 - 390s) / 925

Now, let's substitute y in the first equation:

4 * ((2165 - 390s) / 925) + 56s = 139
(8660 - 1560s) / 925 + 56s = 139
8660 - 1560s + 53200s = 139 \* 925
51640s = 128475 - 8660
51640s = 119815
s = 119815 / 51640
s = 2.319

Now, let's substitute s in the first equation:

4 * y + 56 \* 2.319 = 139
4y + 131.73 = 139
4y = 139 - 131.73
4y = 7.27
y = 7.27 / 4
y = 1.817

So, the solution to the system of equations is s = 2.319 and y = 1.817.
### Answer: s = 2.319, y = 1.817

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 8x7B:

 To solve the pair of simultaneous equations, we can first multiply the first equation by 3 and the second equation by 2 to eliminate the variable z.
3 * (42 * d - 4 * z) = 3 * 75
2 * (40 * d + 45 * z) = 2 * 162

This gives us:
126 * d - 12 * z = 225
80 * d + 90 * z = 324

Adding these two equations together, we get:
206 * d = 549

Dividing both sides by 206, we find that:
d = 549 / 206 = 2.6659...

Substituting this value of d into the first equation, we get:
42 * 2.6659... - 4 * z = 75

Solving for z, we get:
z = (42 * 2.6659... - 75) / 4 = 2.5

Therefore, the values of d and z are approximately 2.67 and 2.5, respectively.
### Answer: d ≈ 2.67, z ≈ 2.5

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 8x7B:

 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 6 and the second equation by 42 to make the coefficients of 'o' the same in both equations:
6*(42 * o) + 6*(24 * a) = 6*142
42*(42 * a) + 42*(6 * o) = 42*75

This gives us:
252 * o + 144 * a = 852
1806 * a + 252 * o = 3150

Now, let's subtract the first equation from the second equation:
1806 * a - 144 * a = 3150 - 852

This simplifies to:
1662 * a = 2298

Now, let's solve for 'a':
a = 2298 / 1662
a = 1.3835616438356164

Since 'a' is not a whole number, there is no solution for this system of equations with integer values for 'a' and 'o'.
### Answer: There is no solution for this system of equations with integer values for 'a' and 'o'.

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 8x7B:

 To solve for p and r, we can first multiply the first equation by 4 and the second equation by 1/2 to eliminate the fraction in the second equation:

4(39r - 2p) = 4(45)
16p - 84r = 18

Now, we have:

39r - 2p = 45
16p - 84r = 18

Next, we can add the two equations to eliminate p:

39r - 2p + 16p - 84r = 45 + 18
14p = 63

Now, we can solve for p:

p = 63 / 14
p = 3

Now, we can substitute p = 3 into the first equation to solve for r:

39r - 2(3) = 45
39r = 48

Now, we can solve for r:

r = 48 / 39
r = 16 / 13

### Answer: p = 3, r = 16 / 13

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 8x7B:

 To solve for the values of 'd' and 'w', we can first isolate one variable in one of the equations and then substitute that expression into the other equation to solve for the other variable.

Let's isolate 'd' in the first equation:

(23 \* d) - (52 \* w) = 7
(23 \* d) = 7 + (52 \* w)
d = (7 + (52 \* w)) / 23

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

(64 \* w) - (8 \* ((7 + (52 \* w)) / 23)) = 58

Solving this equation for 'w' gives:

w = 3

Now, let's substitute 'w' = 3 into the expression for 'd':

d = (7 + (52 \* 3)) / 23
d = 8

Therefore, the values of 'd' and 'w' are:
### Answer: d = 8, w = 3

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 8x7B:

 To solve this system of equations, we can first eliminate either n or z by multiplying one or both of the equations so that the coefficients of n or z are equal in both equations, and then add or subtract the equations to eliminate one of the variables.

Let's first eliminate n.

To do this, we can multiply the first equation by 47 and the second equation by 60, so that the coefficients of n in both equations are equal:

(47 \* (71 \* z) + (60 \* n)) = 47 \* 184
(60 \* (52 \* z) - (47 \* n)) = 60 \* 19

This gives us:

3337z + 2820n = 8728
3120z - 2820n = 1140

Now, if we add these two equations, the n terms will cancel out:

3337z + 2820n + 3120z - 2820n = 8728 + 1140
6457z = 9868

Now, we can solve for z:

z = 9868 / 6457
z = 1.528

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

(71 \* 1.528) + (60 \* n) = 184
109.088 + 60n = 184

Now, we can solve for n:

60n = 184 - 109.088
60n = 74.912
n = 74.912 / 60
n = 1.2485

So, the solution to the system of equations is n = 1.2485 and z = 1.528.
### Answer: n = 1.2485, z = 1.528

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 8x7B:

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

First, let's multiply the first equation by 84 and the second equation by 90 to make the coefficients of e equal in both equations:

5880 * e + 7560 * z = 15984
8910 * z - 7776 * e = 1800

Next, let's add both equations to eliminate e:

(5880 * e + 7560 * z) + (8910 * z - 7776 * e) = 15984 + 1800
5880 * e + 7560 * z + 8910 * z - 7776 * e = 17784
(5880 - 7776) * e + (7560 + 8910) * z = 17784
-1896 * e + 16470 * z = 17784

Now, let's solve for z:

16470 * z = 17784 + 1896 * e
z = (17784 + 1896 * e) / 16470

Next, let's substitute z into the first equation to solve for e:

70 * e + 90 * [(17784 + 1896 * e) / 16470] = 189

Solving this equation, we get:

e = 1

Now, let's substitute e = 1 into the equation for z:

z = (17784 + 1896 * 1) / 16470
z = 1.1

However, since e and z must be integers, this solution is not valid. Therefore, there is no solution for this system of equations.
### Answer: No solution (∃!e,∃!z)

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 8x7B:

 To solve for o and f, we can first isolate one of the variables in the second equation. I'll solve for f:

f = (169 - 11o) / 87

Now, substitute this expression for f into the first equation:

26o - 44((169 - 11o) / 87) = 95

Solve for o:

26o - (44 * 169 / 87 - 44 * 11 / 87 * o) = 95
26o - (7892 / 87 - 484 / 87 * o) = 95
26o - 90 * o = 95 - 7892 / 87
-64o = 95 - 90
o = (95 - 90) / -64
o = -5 / -64
o = 5/64

Now, substitute o = 5/64 into the equation for f:

f = (169 - 11 * 5/64) / 87
f = (169 - 55/64) / 87
f = (169 * 64 - 55) / (64 * 87)
f = 10752 - 55 / 5376
f = 10752 / 5376 - 55 / 5376
f = 10752 / 5376 - 1 / 98
f = (10752 - 5376) / 5376
f = 5376 / 5376
f = 1

So, the solution to the system of equations is o = 5/64 and f = 1.
### Answer: o = 5/64, f = 1

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 8x7B:

 To solve for z and p, we can use the substitution or elimination method. Here, I will use the elimination method.
First, let's multiply the first equation by 58/20 to make the coefficients of p the same in both equations:
40z - 20p = 51 becomes 116z - 58p = 149.4

Now, let's add the two equations:
(116z - 58p) + (6z + 58p) = 149.4 + 165
122z = 314.4

Now, let's solve for z:
z = 314.4 / 122
z = 2.577

Now, let's substitute z = 2.577 into the first equation to solve for p:
40*2.577 - 20*p = 51
103.08 - 20*p = 51
20*p = 103.08 - 51
20*p = 52.08
p = 52.08 / 20
p = 2.604

### Answer: z = 2.577 and p = 2.604.

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 8x7B:

 To solve for s and f, we can use the substitution or elimination method. Here, I will use the elimination method.
First, let's multiply the second equation by 7 to make the coefficients of f the same in both equations:
(3 * f) + (10 * s) = 93 \* 7 = 651

Now, we have:
(71 * s) - (89 * f) = 5
(7 * f) + (70 * s) = 651

Next, let's eliminate f by subtracting the second equation from the first:
(71 * s) - (7 * f) - (70 * s) + (89 * f) = 5 - 651
-6 * f = -646

Now, divide both sides by -6 to solve for f:
f = -646 / -6 = <<-646/-6=107.66666666666667>>107.67 (approximately)

Now, substitute f = 107.67 into the second equation to solve for s:
(3 * 107.67) + (10 * s) = 93
323 + 10s = 93

Subtract 323 from both sides:
10s = 93 - 323 = -230

Divide both sides by 10 to solve for s:
s = -230 / 10 = -23

### Answer: s = -23, f = 107.67 (approximately)

Expected answer: {f: 6553/1103, s: 8292/1103}

Correct? No