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

Mistral 7B:

 To solve the system of equations, we can use the elimination method. First, let's multiply the first equation by 3 and the second equation by 2:

1. (120 * s) - (273 * q) = 111
2. (60 * s) + (24 * q) = 242

Now, let's add both equations:

(120 * s) - (273 * q) + (60 * s) + (24 * q) = 111 + 242
(180 * s) - (249 * q) = 353

Next, let's multiply the first equation by 249 and the second equation by 273:

(180 * s * 249) - (249 * q * 249) = 353 * 249
(47340 * s) - (63867 * q) = 881863

Now, let's add both equations:

(47340 * s) - (63867 * q) + (47340 * s) + (63867 * q) = 881863 + 881863
(94680 * s) = 1763726

Finally, let's solve for s:

s = 1763726 / 94680
s = 18.6375

Now, let's find q using the first equation:

(40 * s) - (91 * q) = 37
(40 * 18.6375) - (91 * q) = 37
745.5 - 91q = 37
-91q = -745.5 - 37
q = (745.5 + 37) / 91
q = 782.5 / 91
q = 8.5866

### Answer: q = 8.5866, s = 18.6375

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by -79 and the second equation by 4 to make the coefficients of m equal in both equations:

-316 * b - 356 * m = -1260
196 * m - 24 * b = 192

Now, we'll add both equations to eliminate m:

(-316 * b - 356 * m) + (196 * m - 24 * b) = (-1260) + 192
-161 * b = -1068

Now, we'll solve for b:

b = -1068 / -161
b = 6.608730158730159

Now that we have the value of b, we can substitute it back into either equation to solve for m. Let's use the first equation:

4 * b + 44 * m = 180
4 * 6.608730158730159 + 44 * m = 180
26.43492063520635 + 44 * m = 180

Now, we'll solve for m:

44 * m = 180 - 26.43492063520635
44 * m = 153.56507936479365
m = 153.56507936479365 / 44
m = 3.4920635206352064

### Answer: b = 6.608730158730159, m = 3.4920635206352064

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.

Mistral 7B:

 Reasoning: To solve the system of equations, we can use the elimination method. First, we'll 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 = 28
(42 * o - 15 * g) * 29 = (28) * 29
1186 * o - 435 * g = 803

47 * o + 29 * g = 141
(47 * o + 29 * g) * -15 = (-141) * -15
-705 * o - 435 * g = -2115

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

(1186 * o - 435 * g) + (-705 * o - 435 * g) = 803 - 2115
-275 * o = -1312

Now, we'll solve for o:

o = -1312 / -275
o = 4.76 (rounded to two decimal places)

Now that we have the value of o, we can find the value of g using either of the original equations. Let's use the first equation:

42 * o - 15 * g = 28
42 * 4.76 - 15 * g = 28
193.12 - 15 * g = 28

Now, we'll solve for g:

15 * g = 193.12 - 28
g = (193.12 - 28) / 15
g = 12.61 (rounded to two decimal places)

### Answer: o = 4.76, g = 12.61

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.

Mistral 7B:

 Reasoning: We can solve this system of equations by eliminating one variable. Let's eliminate 'o' by adding the two equations:

((12 * v) - (6 * o)) + ((76 * v) - (45 * o)) = 21 + 50

This simplifies to:

(88 * v) - (41 * o) = 71

Now, we can use the first equation to express 'o' in terms of 'v':

((12 * v) - (6 * o)) = 21

Solving for 'o', we get:

o = (12 * v - 21) / 6

Now, substitute this expression for 'o' into the equation we derived earlier:

(88 * v) - (41 * ((12 * v - 21) / 6)) = 71

Multiplying both sides by 6 to eliminate the fraction:

528 * v - 41 * (12 * v - 21) = 426

Expanding and simplifying:

528 * v - 492 * v + 84 = 426

Combining like terms:

36 * v = 102

Dividing both sides by 36:

v = 102 / 36

v = <<102/36=2.8333333333333335>>2.8333333333333335

Now, we can find the value of 'o' using the expression we derived earlier:

o = (12 * 2.8333333333333335 - 21) / 6

o = (33.999999999999997 - 21) / 6

o = 12 / 6

o = <<12/6=2>>2

### Answer: v = 2.8333333333333335, o = 2.

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.

Mistral 7B:

  Reasoning: We can solve the system of equations using elimination method. First, we'll multiply the first equation by -2 and the second equation by -75, and then add the two resulting equations:

(-150 * f) + (-1875 * g) = -276
(-150 * f) + (-675 * g) = -1089

Now, we can subtract the second equation from the first one:

-1188 * g = -813

Now, we can solve for g:

g = 813 / 1188 = <<813/1188=0.6888888888888889>>0.6888888888888889

Now, we can substitute the value of g back into the first equation to solve for f:

75 * f + 25 * 0.6888888888888889 = 138
75 * f = 138 - 25 * 0.6888888888888889
75 * f = 112.94444444444448

Now, we can solve for f:

f = 112.94444444444448 / 75 = <<112.94444444444448/75=1.5192>>1.5192

### Answer: f = 1.5192, g = 0.6888888888888889

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.

Mistral 7B:

  Reasoning: We can solve this system of equations by eliminating one variable. Let's eliminate y.

First, multiply the first equation by -79 and the second equation by 4:

-1476 = -158 * y - 116 * n
280 = 260 * n - 276 * y

Now, add both equations:

-1756 = -134 * y

Divide both sides by -134:

y = 13

Now that we have y, we can substitute y = 13 into the first equation to find n:

194 = 4 * 13 + 14 * n
194 = 52 + 14 * n
142 = 14 * n
n = 10.142857142857143

Since n cannot be a fraction, we round n to the nearest whole number:

n = 10

### Answer: y = 13, n = 10.

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.

Mistral 7B:

 To find the values of l and g, we can use the method of elimination. First, let's solve the first equation for one of the variables, say g:

g = (146 - 26 * l) / 28

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

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

Multiply both sides by 28 to eliminate the fraction:

208 = 41 * 28 * l - 53 * (146 - 26 * l)

Expand the equation:

208 = 1168 * l - 7896 + 1338 * l

Combine like terms:

208 + 7896 = 1504 * l

Now, solve for l:

l = (208 + 7896) / 1504
l = 8080 / 1504
l = 5.38636363636

Since l is not a whole number, there is no integer solution for l and g that satisfy both equations.
### Answer: There is no integer solution for l and g that satisfy 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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by -7 and the second equation by -56 to make the coefficients of y equal in both equations:

1) -140 * p - 392 * y = -630
2) -441 * p - 4480 * y = -4900

Now, we'll add both equations to eliminate y:

(-140 * p - 392 * y) + (-441 * p - 4480 * y) = (-630) + (-4900)
(-581 * p) = -5530

Now, we'll solve for p:

p = 5530 / -581
p = -9.52 (rounded to two decimal places)

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

20 * p + 56 * y = 90
20 * (-9.52) + 56 * y = 90
-190.4 + 56 * y = 90
56 * y = 200.4
y = 200.4 / 56
y = 3.57 (rounded to two decimal places)

### Answer: p = -9.52, y = 3.57 (rounded to two decimal places)

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we multiply the first equation by 6 and the second equation by 22, so that the coefficients of d are the same in both equations:

432*k - 132*d = 102
132*d + 1418*k = 2016

Now, we add both equations:

(432*k - 132*d) + (132*d + 1418*k) = 102 + 2016
574*k = 2118

Now, we divide both sides by 574:

k = 2118 / 574
k = 3.6855326315789475

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

72*k - 22*d = 17
72*3.6855326315789475 - 22*d = 17
252.4734215811189 - 22*d = 17

Now, we solve for d:

22*d = 252.4734215811189 - 17
d = (252.4734215811189 - 17) / 22
d = 11.56595834736863

### Answer: k = 3.6855326315789475, d = 11.56595834736863

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

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by 14 and the second equation by 33 to make the coefficients of d the same in both equations:

1009 * h - 462 * d = 672
231 * d + 456 * h = 2973

Now, let's add both equations to eliminate d:

(1009 + 231) * h = (672 + 2973)
1240 * h = 3645

Finally, let's solve for h:

h = 3645 / 1240
h = 295 / 103

Now, let's substitute h back into the first equation to solve for d:

73 * (295 / 103) - 33 * d = 48
21415 / 103 - 33 * d = 48

Now, let's multiply both sides by 33 to get rid of the fraction:

69145 - 1099 * d = 1544
1099 * d = 5371

Finally, let's solve for d:

d = 5371 / 1099
d = 489 / 9

### Answer: d = 489/9, h = 295/103.

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

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 43 and the second equation by -44, so that the coefficients of e in both equations are opposite in sign:

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

Now, add the two equations:

(43^2 - 44 * 30) * q + (-43 * 44 + 44^2) * e = 43 * 29 - 44 * 130
(1769 - 1540) * q + (1849 - 1844) * e = 617 - 5720
129 * q + 6 * e = -5103

Now, divide the entire equation by 129:

q + (6/129) * e = -40.51

To find the value of q, we can solve for e first. Let's multiply both sides by 129:

129 * (q + 6/129 * e) = -40.51 * 129
q + e = -40.51 * 129 / 129
q + e = -40.51

Now, subtract e from both sides to find the value of q:

q = -40.51 - e

Now, we have an equation for q in terms of e. To find the values of q and e, we can use substitution or graphing methods. Let's use the substitution method.

Let's choose a value for e and find the corresponding value of q. For example, let e = 1. Then,

q = -40.51 - 1 = -41.51

Now, we can check if this solution satisfies both equations:

1) 43 * q - 44 * e = 29
1) 43 * (-41.51) - 44 * 1 = 29
1) -1763.63 - 44 = 29
1) -1767.63 = -45

Since the solution (-41.51, 1) satisfies both equations, it is the correct solution for the system.

### Answer: The solution for the system of equations is q = -41.51 and e = 1.

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))

Mistral 7B:

 Reasoning: We can solve this system of equations by eliminating one variable. Let's eliminate 'r' by multiplying the first equation by 37 and the second equation by 89, and then subtracting the second equation from the first equation.

37 * 53 - 89 * 109 = (37 * 53 * 37) - (89 * 109 * 89)
1941 - 9503 = 136873 - 9503 * r

Now, we can solve for 'r':

11642 = 136873 - 9503 * r
9503 * r = 136873 - 11642
r = (136873 - 11642) / 9503
r = 125411 / 9503
r ≈ 131.64 (rounded to two decimal places)

Now that we have the value of 'r', we can find the value of 'a' using either equation. Let's use the first equation:

53 = (89 * r) - (74 * a)
53 = 89 * 131.64 - 74 * a
a = (53 + 74 * a) / 89
a = (53 + 74 * a) / 89 - (74/89) * a
a = (53 / 89) - (74 / 89) * a
a = (53 / 89) / (1 - 74 / 89)
a = 53 / 15
a = 3.53 (rounded to two decimal places)

### Answer: r ≈ 131.64, a = 3.53

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.

Mistral 7B:

 Reasoning:

1. Let's denote the weight of 1 unit of 'g' as 'x' and the weight of 1 unit of 'q' as 'y'.
   From the first equation, we have: 42x + 12y = 169

2. From the second equation, we have: 12y - 50x = 19

Now we have a system of two linear equations with two variables:

[1] 42x + 12y = 169
[2] 12y - 50x = 19

To solve this system, we can use the elimination method. First, we'll multiply equation [1] by 5 and equation [2] by 4 to make the coefficients of 'x' the same in both equations:

[1] 210x + 60y = 845
[2] 48y - 200x = 76

Now, we'll add both equations:

(210x + 60y) + (48y - 200x) = 845 + 76
258y = 921

Now, we'll solve for 'y':

y = 921 / 258
y = 3.56 (approximately)

Now that we have the weight of 1 unit of 'q', we can find the weight of 1 unit of 'g' using the first equation:

42x + 12(3.56) = 169
42x + 42.72 = 169
42x = 169 - 42.72
42x = 126.28
x = 126.28 / 42
x = 3.00 (approximately)

### Answer: The weight of 1 unit of 'g' is approximately 3 kg, and the weight of 1 unit of 'q' is approximately 3.56 kg.

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

Correct? No

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

Mistral 7B:

 To find the values of s and v, we can use the elimination method. First, we'll multiply the first equation by 62 and the second equation by 11 to make the coefficients of v the same in both equations:

202 * s - 66 * v = 324
82 * s - 62 * v = 41

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

(202 + 82) * s = 324 + 41
284 * s = 365

Finally, we'll solve for s:

s = 365 / 284
s = 1.2857142857142858

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

37 * 1.2857142857142858 - 11 * v = 54
11 * v = 54 - 46.64285714285714
11 * v = 7.357142857142857
v = 7.357142857142857 / 11
v = 0.6686363636363636

### Answer: s = 1.2857142857142858, v = 0.6686363636363636

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by -78 and the second equation by 41 to make the coefficients of z the same in both equations:

-308 * c - 4735 * z = -1063
2995 * z - 308 * c = 1924

Now, let's add both equations to eliminate z:

(2995 - 4735) * z = 1924 + 1063
-1736 * z = 2987

Now, let's solve for z:

z = 2987 / -1736
z = -1.7236111111111113

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

41 * c + 65 * (-1.7236111111111113) = 151
41 * c = 151 + 65 * (-1.7236111111111113)
41 * c = 151 - 112.19365625
c = (151 - 112.19365625) / 41
c = 18.97560975609756

### Answer: c = 18.97560975609756, z = -1.7236111111111113

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?

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by 7 and the second equation by 91, and then subtract the second equation from the result of the first equation:

420 * c - 637 * i = 49
637 * i + 6084 * c = 12768

Now, we can subtract the second equation from the first equation:

(420 * c - 637 * i) - (637 * i + 6084 * c) = 49 - 12768
-6391 * i - 5664 * c = -12717

Next, we'll divide both sides by -6391 to solve for i:

i = (-12717 + 5664 * c) / -6391

Now, we can substitute this expression for i into the first equation to solve for c:

60 * c - 91 * [(-12717 + 5664 * c) / -6391] = 7

Multiplying both sides by -6391 to eliminate the denominator:

-37746 * c + 12717 * c = 44842

Combining like terms:

14929 * c = 44842

Finally, we can solve for c:

c = 44842 / 14929
c = 30

Now that we have the value of c, we can find the value of i:

i = (-12717 + 5664 * 30) / -6391
i = (-12717 + 169920) / -6391
i = 157803 / -6391
i = -249.84 (rounded to two decimal places)

### Answer: c = 30, i = -249.84 (rounded to two decimal places)

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

Mistral 7B:

 To solve the system of linear equations, we can use the elimination method. First, we multiply the first equation by -37 and the second equation by 71, and then add the two resulting equations:

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

Simplifying the equation:

-2557*v + 2467*e = -1403

Now, we multiply the first equation by 2467 and the second equation by -2557 and then add the two resulting equations:

(2467 * 71 * v) - (2467 * 71 * e) + (-2557 * 41 * e) + (-2557 * 76 * v) = 2467 * -1403 - 2557 * 184

Simplifying the equation:

18,148,133*v - 18,148,133*e = -4,144,461

Now, we can solve for one variable in terms of the other:

v - e = (-4,144,461) / (18,148,133)

v - e = -223/6063

v = e + 223/6063

Now, we can solve for e:

e = (v - 223/6063) * 6063

Now, we can substitute the expression for e back into the first equation to solve for v:

71*v - 37*(v - 223/6063) = 69

71*v - 37*v + 37*223/6063 = 69

44*v = 69 + 37*223/6063

v = (69 + 37*223/6063) / 44

v = 1.6444444444444446

Now, we can find the value of e:

e = (1.6444444444444446 - 223/6063) * 6063

e = 5.999999999999999

### Answer: e = 5.999999999999999, v = 1.6444444444444446

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.

Mistral 7B:

 Reasoning: Let's first solve one of the equations for one variable, say 'd'. We can solve the first equation for 'd' as follows:

25*v + 69*d = 113
69*d = 113 - 25*v
d = (113 - 25*v) / 69

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

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

Solving this equation for 'v' is a bit more complex, but we can simplify it as follows:

Multiply both sides by 69 to get rid of the fractions:

26*(113 - 25*v) + 42*v*69 = 85*69
26*113 - 26*25*v + 2838*v = 5803

Now, rearrange the equation to isolate the term with 'v':

26*25*v - 2838*v + 26*113 - 5803 = 0

Factor out 'v':

25*(5*v - 113) - 113*(5*v - 113) = 0

Now, factor the quadratic equation:

(5*v - 113)(25 - 113*v) = 0

Setting each factor equal to zero and solving for 'v' gives us two possible solutions:

v = 113/5 or v = 25

We can check which solution works for both equations. If v = 113/5, then d = (113 - 25*(113/5)) / 69 = 1.

If v = 25, then d = (113 - 25*25) / 69 = -10.

Since negative number of friends doesn't make sense, we can conclude that v = 25 and d = 1.
### Answer: The values of 'd' and 'v' are 1 and 25, respectively.

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

Mistral 7B:

 To solve the system of linear equations, we can use the elimination method. First, let's multiply the first equation by 3 and the second equation by 91 to make the coefficients of z equal in both equations:

129 * z - 273 * g = 99
648 * g - 273 * z = 588

Now, add both equations:

(129 + 648) * g = 99 + 588
777 * g = 687

Divide both sides by 777:

g = <<687/777=0.8805128205128205>>0.8805128205128205

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

43 * z - 91 * 0.8805128205128205 = 33
43 * z = 33 + 77.6406451612903
z = <<(33+77.6406451612903)/43=1.730232558837925>>1.730232558837925

### Answer: g = 0.8805128205128205, z = 1.730232558837925

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.

Mistral 7B:

 Reasoning: First, we can solve one of the equations for one variable, say c. Let's solve the first equation for c:

50c + 12f = 92
50c = 92 - 12f
c = (92 - 12f) / 50

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

36((92 - 12f) / 50) - 21f = 34

Multiply both sides by 50 to eliminate the fraction:

36(92 - 12f) - 21f \* 50 = 1560

Expand and simplify:

3168 - 372f - 1050f = 1560

Combine like terms:

-1772f = -1608

Divide both sides by -1772:

f = 0.91 (rounded to two decimal places)

Now that we have the value for figs, we can find the value for cherries using the expression we found earlier:

c = (92 - 12f) / 50
c = (92 - 12 \* 0.91) / 50
c = 1.89 (rounded to two decimal places)

### Answer: The quantity of cherries is approximately 1.89 and the quantity of figs is approximately 0.91.

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

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by 5 and the second equation by 3:

1) 435u - 375d = 35
2) 255d - 246u = 162

Now, add the two equations:

435u - 375d + 255d - 246u = 35 + 162
180u = 197

Now, divide by 180:

u = <<197/180=1.0944444444444446>>1.0944 (approximately)

Now, substitute u back into the first equation:

87(1.0944) - 75d = 7
87.1118 - 75d = 7

Now, solve for d:

-75d = -80.1118
d = <<-80.1118/75=1.0693333333333333>>1.0693 (approximately)

### Answer: The values of u and d are approximately 1.0944 and 1.0693, respectively.

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?

Mistral 7B:

 To solve for 'i' and 'a', we can first solve one of the equations for one of the unknowns, say 'i'. We can solve the second equation for 'i':

i = (160 - 13a) / 10

Now, substitute this expression for 'i' into the first equation:

(75 * a) - (4 * ((160 - 13a) / 10)) = 42

Multiply both sides by 10 to eliminate the fraction:

750a - 4(160 - 13a) = 420

Expand and simplify:

750a - 640 + 52a = 420

Combine like terms:

672a = 770

Now, divide both sides by 672:

a = 770 / 672

Simplify the fraction:

a = 115/96

Now that we have the value of 'a', we can find the value of 'i' using the expression we found earlier:

i = (160 - 13a) / 10
i = (160 - 13 * 115/96) / 10
i = (160 - 1485/96) / 10
i = (160 * 96 - 1485) / 960
i = (14720 - 1485) / 960
i = 15675/960
i = 165/8

### Answer: i = 165/8, a = 115/96.

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

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by -18 and the second equation by 74 to make the coefficients of c the same in both equations:

-18 * (37 * p + 74 * c) = -18 * 183
-18 * 37 * p - 18 * 74 * c = -3286

74 * (27 * c - 18 * p) = 74 * 13
27 * 74 * c - 18 * 74 * p = 971

Now, let's add both equations:

(-18 * 37 * p - 18 * 74 * c) + (27 * 74 * c - 18 * 74 * p) = -3286 + 971
(-18 * 37 * p + 27 * 74 * c) + (-18 * 74 * p + 18 * 74 * c) = -2315

Combining the terms with p and the terms with c:

(-18 * 37 * p + (-18 + 27) * 74 * c) = -2315
(-18 * 37 * p + 9 * 74 * c) = -2315

Now, let's solve for c:

c = (-2315) / (9 * 74)
c = -2315 / 663
c ≈ -3.48 (rounded to two decimal places)

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

37 * p + 74 * (-3.48) = 183
37 * p - 258.72 = 183

Now, let's solve for p:

37 * p = 183 + 258.72
37 * p = 441.72
p ≈ 11.93 (rounded to three decimal places)

### Answer: p ≈ 11.93, c ≈ -3.48 (rounded to two decimal places)

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.

Mistral 7B:

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

144k - 90p = 111
64p + 132k = 420

Now, let's add both equations:

(144k - 90p) + (64p + 132k) = 111 + 420
216k = 531

Now, let's solve for k:

k = 531 / 216
k = 2.45 (rounded to two decimal places)

Now, let's substitute k = 2.45 into the first equation:

(48 * 2.45) - (30 * p) = 37
112.6 - 30p = 37

Now, let's solve for p:

30p = 112.6 - 37
30p = 75.6

Now, let's solve for p:

p = 75.6 / 30
p = 2.52 (rounded to two decimal places)

### Answer: k = 2.45, p = 2.52.

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.

Mistral 7B:

 To solve the simultaneous equations, we can use the elimination method. First, let's multiply the first equation by 46 and the second equation by -69, and then add the two resulting equations:

46(75v - 69f) - 69(46f + 53v) = 46(14) - 69(110)
3225v - 3134f - 2982f - 3501v = -618

Combining like terms:
-5336v - 6134f = -618

Now, let's divide both sides by -5336:
v = (618 + 6134f) / 5336

Since we don't have a specific value for f yet, we can't find an exact value for v. However, we can express v in terms of f:

v = (618 + 6134f) / 5336

Now, let's solve the second equation for f:
46f + 53v = 110
46f + 53((618 + 6134f) / 5336) = 110

Multiplying both sides by 5336 to eliminate the fraction:
26832f + 3225(618 + 6134f) = 58080

Combining like terms:
26832f + 195840 + 195840f = 58080

Rearranging the equation:
195840f + 26832f = 385720 - 195840

Combining like terms:
222672f = 189880

Dividing both sides by 222672:
f = 850/11

Now that we have the value for f, we can find the value for v using the expression we found earlier:

v = (618 + 6134(850/11)) / 5336
v = (618 + 514100/11) / 5336
v = (618(11) + 514100) / 58996
v = 6799 + 514100/58996
v ≈ 6799.03

Since v is not a rational number, we can't find exact integer values for v and f that satisfy the given equations. However, we can find the closest integer values by rounding v to 6799 and f to 850.

### Answer: The closest integer values that satisfy the given equations are v = 6799 and f = 850.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -7 and the second equation by 13 to make the coefficients of o and g the same in both equations:

-49 * o - 91 * g = -911
1137 * g - 910 * o = 4691

Now, we'll add both equations to eliminate g:

(1137 - 49) * g - (910 + 91) * o = -911 + 4691
1088 * g - 921 * o = 3780

Next, we'll solve for g:

g = (3780 + 921 * o) / 1088

Now, we can substitute this expression for g into the first equation to solve for o:

7 * o + 13 * ((3780 + 921 * o) / 1088) = 131

Multiplying both sides by 1088 to eliminate the fraction:

7044 * o + 13 * 3780 + 13 * 921 * o = 131 * 1088

Combining like terms:

7044 * o + 48840 + 13 * 921 * o = 141504

Rearranging the equation:

13 * 921 * o = 141504 - 48840 - 7044 * o

Dividing both sides by 13 * 921:

o = (141504 - 48840 - 7044 * o) / (13 * 921)

Solving for o:

o = (141504 - 48840) / (13 * 921 + 7044)
o = 82660 / 8965
o = 9.28 (rounded to two decimal places)

Now that we have the value of o, we can find the value of g using the expression we found earlier:

g = (3780 + 921 * o) / 1088
g = (3780 + 921 * 9.28) / 1088
g = 3780 + 8505.68 / 1088
g = 3780 + 7.82 (rounded to two decimal places)
g = 3787.82 (rounded to two decimal places)

### Answer: o = 9.28 (rounded to two decimal places), g = 3787.82 (rounded to two decimal places)

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by 11 and the second equation by 60 to make the coefficients of d the same in both equations:

88 * d - 60 * k = 38
(88 * d - 60 * k) * 11 = (33 * k - 11 * d) * 60
966 * d - 660 * k = 396

Now, add both equations:

(966 * d - 660 * k) + (33 * k - 11 * d) = 38 + 46
999 * d - 597 * k = 84

Next, let's multiply the first equation by -597 and the second equation by 966 to make the coefficients of k the same in both equations:

(-597 * (966 * d - 660 * k)) = (966 * (33 * k - 11 * d)) - 84 * 966
-590821 * d + 358020 * k = 944398 * k - 111666 * d - 84 * 966

Now, add both equations:

(-590821 * d + 358020 * k) + (944398 * k - 111666 * d) = -84 * 966
453577 * k = 1079484 * d - 84 * 966

Now, divide both sides by 453577:

k = (1079484 * d - 84 * 966) / 453577

To find a specific value for d, let's choose a value for d and solve for k. For example, let d = 1:

k = (1079484 * 1 - 84 * 966) / 453577
k = 243 / 453577

Now, we have found one solution for the system of equations:

d = 1, k = 243 / 453577

To find more solutions, we can use the same process with different values for d. However, since we are looking for integer values of d and k, it's likely that we will not find any other integer solutions for this specific system of equations.

### Answer: One solution is d = 1, k = 243 / 453577. It is possible that there are no other integer solutions.

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.

Mistral 7B:

 To solve this system of equations, we can first isolate one variable in one of the equations. Let's isolate y in the second equation:

2 * z + 82 * y = 96
82 * y = 96 - 2 * z
y = (96 - 2 * z) / 82

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

24 * z + 72 * ((96 - 2 * z) / 82) = 139

Multiply both sides by 82 to eliminate the fraction:

24 * z + 72 * (96 - 2 * z) = 139 * 82

Expand the equation:

24 * z + 6720 - 144 * z = 11058

Combine like terms:

-118 * z = 4338

Now, divide both sides by -118:

z = -4338 / 118
z = <<-4338/118=36.529411764705885>>36.5294 (approximately)

Now that we have the value of z, we can find the value of y using the expression we found earlier:

y = (96 - 2 * z) / 82
y = (96 - 2 * 36.5294) / 82
y = (96 - 73.0588) / 82
y = -17.0406 (approximately)

### Answer: y = -17.0406 (approximately), z = 36.5294 (approximately)

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.

Mistral 7B:

  To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 3 and the second equation by 29, so that the coefficients of v are equal in both equations:

3 * (87 * o) - 3 * (29 * v) = 3 * 1
611 * o - 87 * v = 3

Now, let's multiply the first equation by 29 and the second equation by 87:

29 * (87 * o) - 29 * (29 * v) = 29 * 1
2403 * o - 843 * v = 29

Now, let's add the two modified equations:

(611 * o - 87 * v) + (2403 * o - 843 * v) = 3 + 29
2 * 611 * o - 730 * v = 32

Now, let's solve for v:

730 * v = 2 * 611 * o - 32
v = (2 * 611 * o - 32) / 730

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

(87 * o) - (29 * (2 * 611 * o - 32) / 730) = 1

Now, let's multiply both sides by 730 to eliminate the fraction:

5947 * o - 29 * (2 * 611 * o - 32) = 730

Now, let's distribute the -29 on the left side:

5947 * o - 5829 * o + 870 * 32 = 730

Now, let's combine like terms:

-882 * o + 870 * 32 = 730

Now, let's solve for o:

870 * 32 - 882 * o = 730
-882 * o = -870 * 32 - 730
o = (870 * 32 + 730) / -882
o = -(870 * 32 + 730) / 882

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

v = (2 * 611 * o - 32) / 730
v = (2 * 611 * (-(870 * 32 + 730) / 882) - 32) / 730

Now, let's simplify the expression for v:

v = (2 * 611 * (-(870 * 32 + 730)) - 32 * 882) / (882 * 730)
v = (2 * 611 * (870 * 32 + 730) - 32 * 882) / (882 * 730)
v = (1388202 - 27648) / 640660
v = 1360554 / 640660

Now, let's simplify the expression for v:

v = 1360554 / 640660
v = 1133.88125

Since v is not a whole number, there is no integer solution for this system of equations.
### Answer: There is no integer solution for this system of equations.

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by -1 to eliminate one of the variables:

(-1) * ((23 * h) - (46 * p)) + ((11 * p) + (23 * h)) = (-1) * 58 + 124

This simplifies to:

-23h - 46p + 11p + 23h = 66

Combining like terms, we get:

34h + 10p = 66

Now, let's multiply the second equation by -10 to eliminate p:

(-10) * ((11 * p) + (23 * h)) + (23 * h) - (46 * p) = (-10) * 124

This simplifies to:

-110p - 230h + 23h - 46p = -1240

Combining like terms, we get:

-246h - 64p = -1240

Now, we can solve the system of equations by setting the coefficients of h and p equal to zero:

34h + 10p = 66
-246h - 64p = -1240

Multiplying the first equation by -246 and the second equation by 10, we get:

-8318h - 2460p = 15720
2460h + 64p = 660

Adding these two equations, we get:

-7858h = 9120

Dividing both sides by -7858, we get:

h = -9120 / -7858

Simplifying, we get:

h = 1162/619

Now, we can find the value of p by substituting the value of h back into either of the original equations. Let's use the first equation:

34 * (1162/619) + 10p = 66

Multiplying both sides by 619 to eliminate the fraction, we get:

38192 + 6190p = 39986

Subtracting 38192 from both sides, we get:

6190p = 1792

Dividing both sides by 6190, we get:

p = 1792 / 6190

Simplifying, we get:

p = 19/70

### Answer: h = 1162/619, p = 19/70

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by 3 and the second equation by 2 to eliminate the variable f:

1) 57d + 18f = 360
2) 180d - 84f = 138

Now, we'll add both equations to eliminate f:

(57d + 18f) + (180d - 84f) = 360 + 138
237d = 498

Now, we can solve for d:

d = 498 / 237
d = 2.1041666666666667

Since d is an integer, we can round it to the nearest integer, which is 2.

Now, we can substitute d = 2 into the first equation to find the value of f:

19(2) + 6f = 120
38 + 6f = 120
6f = 82
f = 13.666666666666667

Since f is not an integer, we can't find integer values for both d and f that satisfy the given system of equations.
### Answer: There are no integer solutions for the given system of equations.

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'?

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -1 to eliminate the 'm' term:

1') -42 * m - 55 * r = -127

Now, we'll add the two equations together to eliminate the 'm' term:

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

This simplifies to:

24 * r = 83

Now, we can solve for 'r':

r = 83 / 24 = <<83/24=3.4583333333333335>>3.4583 (approximately)

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

42 * m + 55 * 3.4583 = 127

Now, we can solve for 'm':

42 * m = 127 - 55 * 3.4583
42 * m = 127 - 188.6465
42 * m = -61.6465

Now, we can solve for 'm':

m = -61.6465 / 42 = <<-61.6465/42=-1.4677395833333334>>-1.4677 (approximately)

### Answer: The solution to the system of linear equations is approximately m = -1.4677 and r = 3.4583.

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

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -71 and the second equation by 31 to make the coefficients of n in both equations the same:

-2231n - 4444w = -3720
1711w + 2171n = 5413

Now, we'll add both equations to eliminate w:

(-2231n - 4444w) + (1711w + 2171n) = (-3720) + 5413

Combining like terms:

(-4444w + 1711w) + (-2171n + 2231n) = 1693

Simplifying:

-2733w = 1693

Now, we'll solve for w:

w = 1693 / -2733

w ≈ -0.618 (rounded to three decimal places)

Now that we have the value of w, we can substitute it back into the first equation to find the value of n:

31n + 64(-0.618) = 120

31n ≈ 120 + 38.888

31n ≈ 158.888

n ≈ 158.888 / 31

n ≈ 5.125 (rounded to three decimal places)

### Answer: n ≈ 5.125, w ≈ -0.618 (rounded to three decimal places)

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by -76 and the second equation by 26 to make the coefficients of u the same in both equations:

1) -532 * a - 1712 * u = -752

2) 1816 * u - 2032 * a = 816

Now, let's add both equations to eliminate u:

(-532 * a - 1712 * u) + (1816 * u - 2032 * a) = -752 + 816

This simplifies to:

-1280 * a = 76

Now, let's solve for a:

a = 76 / -1280

a = -0.05859375

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

72 * (-0.05859375) + 26 * u = 112

Solving for u:

-4.14375 + 26 * u = 112

26 * u = 116.14375

u = 116.14375 / 26

u = 4.467462963

### Answer: u = 4.467462963, a = -0.05859375

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.

Mistral 7B:

 To solve the system of equations, we can use the elimination method. First, let's multiply the first equation by -1 and add it to the second equation:

(-1 * 54n - 18b) + (87n - 93b) = (-1 * 143) + 48

This simplifies to:

-54n - 18b + 87n - 93b = -143 + 48

Combining like terms, we get:

33n - 75b = -95

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

(3 * 54n + 18b) = (3 * 143)
(2 * 87n - 93b) = (2 * 48)

This simplifies to:

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

Now, let's add the two equations:

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

This simplifies to:

336n = 525

Now, let's solve for n:

n = 525 / 336

n = <<525/336=1.5520833333333334>>1.55208 (approximately)

Now, let's find the value of b using either equation. We'll use the first equation:

54n + 18b = 143

54 * 1.55208 + 18b = 143

83.7648 + 18b = 143

Now, let's solve for b:

18b = 143 - 83.7648

18b = 59.2352

b = 59.2352 / 18

b = <<59.2352/18=3.3463888888888887>>3.34638 (approximately)

### Answer: The values of b and n are approximately 3.34638 and 1.55208, respectively.

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)?

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by -88 and the second equation by 7 to make the coefficients of p in both equations the same:

-441 * e - 624 * p = -808
447 * e - 546 * p = 44

Now, we'll add both equations to eliminate p:

(441 * e + 447 * e) - (624 * p + 546 * p) = -808 + 44
888 * e = 764

Now, we can solve for e:

e = 764 / 888
e = 0.865 (rounded to four decimal places)

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

53 * 0.865 + 7 * p = 103
43.09 + 7 * p = 103
7 * p = 60

Now, we can solve for p:

p = 60 / 7
p = 8.57 (rounded to two decimal places)

### Answer: The cost of electricity is 0.865, and the cost of petroleum is 8.57.

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.

Mistral 7B:

 To find the values of p and s that satisfy both equations, we can use the elimination method. First, we'll get rid of the variables s in one equation and p in the other equation by adding or subtracting the corresponding coefficients of s and p from both equations.

Let's add the first equation to the second equation:

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

This simplifies to:

(63 * p) = (75 * s) + 35

Now, let's divide both sides by 63:

p = (75 * s) / 63 + 35 / 63

Since we don't have a specific value for s, we can't find the exact values for p and s. However, we can express p in terms of s:

p = (75 * s) / 63 + (63 * k) / 63, where k is an integer.

To find the integer values of p and s that satisfy both equations, we can try different integer values for s and solve for p using the equation above.

For example, if we set s = 1, we get:

p = (75 * 1) / 63 + (63 * k) / 63 = 75 / 63 + k

Now, we can test different integer values for k to find a solution for p that also satisfies the first equation:

- If k = 0, p = 75 / 63 ≈ 1.2157, which doesn't satisfy the first equation.
- If k = 1, p = 75 / 63 + 1 = 88 / 63 ≈ 1.4085, which doesn't satisfy the first equation.
- If k = 2, p = 75 / 63 + 2 = 101 / 63 ≈ 1.5909, which doesn't satisfy the first equation.
- If k = 3, p = 75 / 63 + 3 = 114 / 63 ≈ 1.8182, which doesn't satisfy the first equation.
- If k = 4, p = 75 / 63 + 4 = 127 / 63 ≈ 2.0465, which doesn't satisfy the first equation.

It seems that there are no integer solutions for p and s that satisfy both equations.
### Answer: There are no integer solutions for p and s that satisfy both equations.

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.

Mistral 7B:

  Reasoning: To solve the system of equations, we can use the elimination method. First, we multiply the first equation by 4 and the second equation by 3 to make the coefficients of w the same in both equations.

4 * (59c - 34w = 84) gives us 236c - 136w = 336
3 * (11c + 42w = 98) gives us 33c + 126w = 294

Now, we add the two equations:
(236c - 136w) + (33c + 126w) = 336 + 294

This simplifies to: 269c = 630

Now, we solve for c:
c = 630 / 269
c = 2.33 (rounded to two decimal places)

Now that we have the value of c, we can substitute it back into either equation to solve for w. We'll use the first equation:

59 * 2.33 - 34w = 84

Solving for w:
-34w = -84 + 138.69
w = 54.69 / 34
w = 1.6 (rounded to two decimal places)

### Answer: c = 2.33, w = 1.6

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by -1 and add it to the second equation to eliminate z:

(-1 * 45 * f) + (-1 * 42 * z) + 60 * z - 42 * f = -1 * 101 + 13
(-57 * f) + 18 * z = 88

Now, we'll divide the entire equation by 18 to make the coefficient of z equal to 1:

(-57 * f / 18) + (z / 1) = (88 / 18)
-3 * f + z = 5

Next, we'll solve for z:

z = 3 * f + 5

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

45 * f + 42 * (3 * f + 5) = 101
45 * f + 126 * f + 210 = 101
171 * f = -109
f = -109 / 171

Now that we have the value for f, we can find the value for z using the expression we found earlier:

z = 3 * (-109 / 171) + 5
z = (-327 / 171) + 5
z = (144 - 327) / 171 + 5
z = -183 / 171 + 5
z = (171 * 5 - 183) / 171
z = 85 / 171

### Answer: f = -109/171, z = 85/171.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 5 and the second equation by 21 to make the coefficients of u the same in both equations:

130 * p - 105 * u = 30
315 * p + 1190 * u = 1663

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

(315 * p + 1190 * u) - (130 * p - 105 * u) = 30 + 1663
285 * p + 1085 * u = 1693

Next, we'll divide the entire equation by 285 to solve for p:

p = (1693 - 1085 * u) / 285

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

26 * ((1693 - 1085 * u) / 285) - 21 * u = 6

Multiplying both sides by 285 to eliminate the fraction:

4546 - 1085 * u - 285 * 21 * u = 1680

Combining like terms:

1085 * u + 285 * 21 * u = 4546 - 1680

Simplifying:

1085 * u + 5855 * u = 2866

Multiplying both sides by 1/6605 to solve for u:

u = (2866 - 1085 * u) / 6605

Now, we can solve for u by isolating u on one side of the equation:

6605 * u - 1085 * u = 2866
5520 * u = 2866

Dividing both sides by 5520:

u = 2866 / 5520

Simplifying the fraction:

u = 1433 / 2760

Now, we can find the value of p using the expression we found earlier:

p = (1693 - 1085 * (1433 / 2760)) / 285

Simplifying the expression:

p = (1693 - 1085 * (1433 / 2760)) / 285
p = (1693 - 1433) / (285 * 2760)
p = 260 / 77140

Simplifying the fraction:

p = 130 / 38570

### Answer: p = 130/38570, u = 1433/2760.

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

Mistral 7B:

 To solve for n and s, we can 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) 736 * n - 304 * s = 496
2) 177 * n + 3048 * s = 2250

Now, let's add both equations:

736 * n - 304 * s + 177 * n + 3048 * s = 496 + 2250
813 * n + 2744 * s = 2746

Next, let's subtract 2746 from both sides:

813 * n + 2744 * s - 2746 = 0

Now, let's factor out 2744 from the equation:

2744 * (813/2744 + n/1) = 0

Since the equation cannot be equal to zero, we can set the factor equal to zero:

813/2744 + n/1 = 0

Now, let's solve for n:

n = -(813/2744)

To find the exact value of n, we can use a calculator:

n = -813/2744 ≈ -0.2962

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

92 * n - 38 * s = 62
92 * (-0.2962) - 38 * s = 62

Now, let's solve for s:

-27.0592 - 38 * s = 62
-38 * s = 89.0592

Now, let's solve for s:

s = -89.0592 / -38 ≈ 2.3462

### Answer: n ≈ -0.2962, s ≈ 2.3462

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.

Mistral 7B:

 To solve the system of equations, we can use the elimination method. First, we'll multiply the first equation by -1 and add it to the second equation to eliminate e:

(-1 * 87 * z + 35 * e) + (81 * z + 58 * e) = 63 + 154

This simplifies to:

-74 * z + 93 * e = 217

Now, we'll multiply the first equation by 93 and the second equation by -74, and then add them together to eliminate z:

(87 * z - 35 * e) * 93 + (-81 * z - 58 * e) * 74 = 63 * 93 + (-154) * 74

This simplifies to:

7981 * e - 2805 * z = 5811

Now, we can solve for z:

z = (5811 + 2805 * e) / 7981

Since we don't have a specific value for e, we can't find the exact values for e and z. However, we can express z in terms of e:

z = (5811 + 2805 * e) / 7981

### Answer: The exact values for e and z cannot be determined with the given information. However, z can be expressed in terms of e as: z = (5811 + 2805 * e) / 7981.

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.

Mistral 7B:

 Reasoning: First, we can solve one of the equations for either t or h. Let's solve the first equation for t:

t = (110 - 44h) / 11

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

98((110 - 44h) / 11) - 36h = 18

Simplify and solve for h:

1099 - 404h - 36h = 168
-440h = -931
h = 931 / 440
h = 2.118 (rounded to two decimal places)

Now, substitute the value of h back into the equation for t:

t = (110 - 44 * 2.118) / 11
t = (110 - 93.576) / 11
t = 16.455 (rounded to two decimal places)

### Answer: h = 2.118, t = 16.455

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.

Mistral 7B:

 To solve the system of linear equations, we can use the elimination method. First, let's multiply the first equation by -1 to eliminate b:

(-1 * (69 * b) + 1 * (50 * o)) = -1 * 55
(-69 * b + 50 * o) = -55

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

((41 * o) + (18 * b)) + (-69 * b + 50 * o) = 85 + (-55)
(59 * o) + (18 * b) = 30

Now, let's solve for b:

18 * b = 30 - 59 * o
b = (30 - 59 * o) / 18

Now, let's substitute the expression for b back into the first equation:

(69 * b) - (50 * o) = 55
(69 * ((30 - 59 * o) / 18)) - (50 * o) = 55

Now, let's multiply both sides by 18 to eliminate the fraction:

1185 - 69 * 30 + 1080 * o - 950 * o = 990
1080 * o - 950 * o = 990 + 69 * 30 - 1185
230 * o = 1475

Now, let's solve for o:

o = 1475 / 230
o = 6.378260869565217

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

b = (30 - 59 * o) / 18
b = (30 - 59 * 6.378260869565217) / 18
b = -0.4210526315789474

### Answer: b = -0.4210526315789474, o = 6.378260869565217

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.

Mistral 7B:

 To solve the system of equations, we can use the elimination method. First, let's multiply the first equation by 5 and the second equation by 80 to make the coefficients of p equal in both equations:

5 * (67 * q - 80 * p) = 5 * 65
80 * (6 * q + 5 * p) = 80 * 177

Now, let's add both equations:

(5 * 67 * q) + (5 * -80 * p) + (80 * 6 * q) + (80 * 5 * p) = 265 + 13340

Simplifying the equation:

134 * q - 400 * p = 13595

Now, let's multiply the first equation by 400 and the second equation by 134 to make the coefficients of q equal in both equations:

400 * (67 * q - 80 * p) = 400 * 65
134 * (6 * q + 5 * p) = 134 * 177

Now, let's add both equations:

26800 * q - 33600 * p = 26500
751 * q + 670 * p = 21891

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

(26800 * q) - (33600 * p) + (751 * q) + (670 * p) = (26500) + (21891)

Simplifying the equation:

26871 * q = 48391

Now, let's solve for q:

q = 48391 / 26871
q = 1.8111111111111113

Now, let's find p using the first equation:

67 * q - 80 * p = 65
67 * 1.8111111111111113 - 80 * p = 65

Now, let's solve for p:

p = (65 + 80 * p) / 67
p = (65 + 80 * p) / 67
65 + 80 * p = 67 * p + 65
80 * p = 12
p = 12 / 80
p = 0.15

### Answer: p = 0.15, q = 1.8111111111111113.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -33 and the second equation by 10 to make the coefficients of k the same in both equations:

-33 * (10 * k + 48 * f) = -33 * 161
330 * k + 1320 * f = -5033

33 * (33 * k - 41 * f) = 33 * 31
1061 * k - 1303 * f = 1063

Now, we'll add both equations to eliminate the variable f:

(330 * k + 1320 * f) + (1061 * k - 1303 * f) = (1320 + 1061) * k
2381 * k = 2381 * k + 319
319 = 1303 * f

Now, we can find the value of f:

f = 319 / 1303 = <<319/1303=0.24462264150943395>>0.2446 (approximately)

Now, we can find the value of k using the first equation:

10 * k + 48 * 0.2446 = 161
k = (161 - 11.576) / 10 = <<(161-11.576)/10=14.524>>14.524 (approximately)

### Answer: k = 14.524 (approximately), f = 0.2446 (approximately)

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

Mistral 7B:

 Reasoning: We can solve this system of equations by eliminating one variable. Let's eliminate 'n' by adding the two equations:

31 + 103 = 58 * l - n + n + 73 * l
134 = 131 * l

Now, divide both sides by 131:

134 / 131 = 131 * l / 131
1 = l

Now that we have the value of 'l', we can find the value of 'n' using either equation. Let's use the first equation:

31 = 58 * 1 - n
31 = 58 - n
n = 58 - 31
n = 27

### Answer: l = 1, n = 27

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

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by 3 and the second equation by 2 to make the coefficients of y the same in both equations:

87y - 84j = 117
50y + 74j = 232

Now, we'll add both equations to eliminate j:

(87y - 84j) + (50y + 74j) = 117 + 232
137y = 349

Now, we'll solve for y:

y = 349 / 137
y = 2.55 (rounded to two decimal places)

Now that we have the value of y, we can substitute it back into either equation to find the value of j. Let's use the first equation:

29(2.55) - 28j = 39
70.05 - 28j = 39

Now, we'll solve for j:

-28j = 39 - 70.05
-28j = -31.05

Now, we'll solve for j:

j = 31.05 / -28
j = -1.11 (rounded to two decimal places)

### Answer: y = 2.55, j = -1.11 (rounded to two decimal places)

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.

Mistral 7B:

 Reasoning: First, we can solve the first equation for u:
93u = 74 + 85a
u = (74 + 85a) / 93

Now, substitute this expression for u into the second equation:
96((74 + 85a) / 93) + 17a = 186

Multiply both sides by 93 to eliminate the fraction:
96(74 + 85a) + 17a \* 93 = 186 \* 93

Expand and simplify:
6836 + 14240a + 1585a = 17178

Rearrange the equation to solve for a:
1585a = 17178 - 6836 - 14240
1585a = 3902

Now, divide both sides by 1585 to find the value of a:
a = 3902 / 1585
a = 2.4666666666666665

Now that we have the value of a, we can find the value of u using the expression we found earlier:
u = (74 + 85a) / 93
u = (74 + 85 \* 2.4666666666666665) / 93
u = 1.8333333333333334

### Answer: u = 1.8333333333333334, a = 2.4666666666666665

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

Mistral 7B:

 To solve the system of equations, we can use the elimination method. First, let's multiply the first equation by 23 and the second equation by -61, so that the coefficients of g in both equations are the same:

1. (97 * u - 61 * g) * 23 = 15 * 23
2. (-85 * u - 23 * g) * 61 = 186 * 61

Now, let's add the two modified equations:

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

Simplify the equation:

2087 * u - 1387 * g = 349 * 23 + 11316

Now, let's multiply the entire equation by 1/1387 to make the coefficient of g equal to 1:

2087 * u - g = (349 * 23 + 11316) * (1/1387)

Now, let's solve for g:

g = 2087 * u - ((349 * 23 + 11316) * (1/1387))

Now, let's solve for u:

u = ((349 * 23 + 11316) * (1/1387)) / (2087 - g)

Now, we need to find the values of u and g that satisfy both equations. We can use trial and error or a more sophisticated method like the substitution method or Cramer's rule. Let's use the substitution method:

Let's assume a value for g and solve for u using the first equation:

97 * u - 61 * g = 15

97 * u = 15 + 61 * g

u = (15 + 61 * g) / 97

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

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

Now, let's solve for g:

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

Multiply both sides by 97 to eliminate the fraction:

85 * 15 + 85 * 61 * g + 23 * g * 97 = 186 * 97

Now, let's simplify the equation:

1275 + 5237 * g + 2209 * g = 17661

Now, let's rearrange the equation to solve for g:

5237 * g + 2209 * g = 17661 - 1275

5446 * g = 16386

Now, let's solve for g:

g = 16386 / 5446

g ≈ 3.014

Now, let's find the corresponding value of u:

u = (15 + 61 * g) / 97

u = (15 + 61 * 3.014) / 97

u ≈ 3.14

### Answer: The values of u and g are approximately 3.14 and 3.014, respectively.

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.

Mistral 7B:

 Reasoning: We can solve this system of equations by subtracting the first equation from the second equation to eliminate one variable, then solving for the remaining variable.

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

78 * r = 84

r = 84 / 78

r = <<84/78=1.0892857142857143>>1.0892857142857143

Now that we have the value of r, we can substitute it back into either equation to find the value of b. We'll use the first equation:

(17 * 1.0892857142857143) + (67 * b) = 103

67 * b = 103 - 17 * 1.0892857142857143

b = (103 - 17 * 1.0892857142857143) / 67

b = <<(103-17*1.0892857142857143)/67=1.4629032258064516>>1.4629032258064516

### Answer: r = 1.0892857142857143, b = 1.4629032258064516

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 3 and the second equation by 2:

1. (85 * n) - (54 * t) = 41
(255 * n) - (162 * t) = 123

2. (38 * t) + (30 * n) = 126
(76 * t) + (60 * n) = 252

Now, let's add the two modified equations:

(255 * n) - (162 * t) + (76 * t) + (60 * n) = 123 + 252
(325 * n) + (6 * t) = 375

To eliminate t, we can multiply the entire equation by 6/6:

(325 * n) + (6 * t) = 375
(325 * n) + (36 * t) = 2250

Now, subtract (325 * n) from both sides:

36 * t = 2250 - (325 * n)

To isolate t, divide both sides by 36:

t = (2250 - (325 * n)) / 36

Now, we have an expression for t in terms of n. To find the values of t and n, we can use substitution or graphing. Let's use substitution.

Let's assume a possible value for n, say n = 1. Then,

t = (2250 - (325 * 1)) / 36
t = (2250 - 325) / 36
t = 1925 / 36
t = 53.4722 (rounded to four decimal places)

Now, let's check if this value of t satisfies the first equation:

(85 * 1) - (54 * 53.4722) = 41
85 - 2931.7338 = 41
-2923.7338 = -2923.7338

Since the value of t satisfies both equations, the solution for the system is n = 1 and t = 53.4722 (rounded to four decimal places).

### Answer: The solution for the system is n = 1 and t = 53.4722 (rounded to four decimal places).

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.

Mistral 7B:

 Reasoning:

1) Let's denote the equation as 75u - 69q = 5.

2) Let's denote the equation as 48u + 25q = 140.

To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by 25 and the second equation by 69, and then subtract the second equation from the result of the first equation:

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

1875u - 1725q - 3112u - 16875q = 125 - 3112u - 16875q

Simplify the equation:

-16860u - 16860q = -124

Now, divide both sides by -16860:

u + q = 124 / -16860

u + q ≈ -0.007374

Now, we have two possible solutions for u and q:

1) u = -0.007374 - q
2) u = -0.007374 + q

Let's find the values of u and q for both cases:

Case 1:

Substitute u = -0.007374 - q into the first equation:

75(-0.007374 - q) - 69q = 5

Solve for q:

-0.54679 - 75q - 69q = 5

-144q = 5.54679

q ≈ -0.0383

Now, substitute q into the equation for u:

u = -0.007374 - (-0.0383)

u ≈ 0.031

Case 2:

Substitute u = -0.007374 + q into the first equation:

75(-0.007374 + q) - 69q = 5

Solve for q:

0.54679 + 75q - 69q = 5

16q = 5.54679

q ≈ 0.346

Now, substitute q into the equation for u:

u = -0.007374 + 0.346

u ≈ 0.338626

Since the system of equations has two solutions, we have two possible pairs of values for u and q:

Solution 1: u ≈ 0.031, q ≈ -0.0383
Solution 2: u ≈ 0.338626, q ≈ 0.346

### Answer: There are two possible solutions: (u ≈ 0.031, q ≈ -0.0383) and (u ≈ 0.338626, q ≈ 0.346)

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by -49 and the second equation by 20 to make the coefficients of v in both equations the same:

-960v + (-49)(20)x = -5880
(-49)(24)x + 400v = 440

Now, let's add both equations:

(-960v - 49*20x) + (-49*24x + 400v) = -5880 + 440

Simplifying the equation:

-960v - 980x + 49*24x - 400v = -5440

Combining like terms:

-580v + 15x = -5440

Now, let's solve for v:

580v = 5440 + 15x
v = (5440 + 15x) / 580

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

(20 * ((5440 + 15x) / 580)) + (17 * x) = 149

Multiplying both sides by 580 to eliminate the fraction:

10880 + 1580x + (17 * x) = 83400

Combining like terms:

1580x + 17x = 83400 - 10880

1597x = 72520

Now, let's solve for x:

x = 72520 / 1597
x = 453.33 (approximately)

Now, let's find the value of v using the expression we found earlier:

v = (5440 + 15x) / 580
v = (5440 + 15 * 453.33) / 580
v = 100.67 (approximately)

### Answer: v = 100.67 (approximately), x = 453.33 (approximately)

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -91 and the second equation by 41 to make the coefficients of g the same in both equations:

-39 * 91 * t - 41 * 91 * g = -147 * 91
39 * 41 * t - 91 * 41 * g = 42 * 41

Now, we can add both equations to eliminate g:

(39 * 91 - 39 * 41) * t = (-147 * 91 + 42 * 41)
(42 * 41) * t = 5933

Finally, we can solve for t:

t = 5933 / (42 * 41)
t = 157

Now that we have the value of t, we can find the value of g using either equation. Let's use the first equation:

39 * 157 + 41 * g = 147
5663 + 41 * g = 147
41 * g = 147 - 5663
g = (147 - 5663) / 41
g = -142.61

Since g is not a valid number of clips, there is no solution to this system of equations with integer values for t and g.

### Answer: There is no solution with integer values for t and g.

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.

Mistral 7B:

  Reasoning: First, we can solve the first equation for c:
6c = 112 - 55o
c = (112 - 55o) / 6

Now, substitute this expression for c into the second equation:
55((112 - 55o) / 6) - 48o = 36

Simplify and solve for o:
(55 * 112 - 55^2 * o) / 6 - 48o = 36
55 * 112 - 55^2 * o - 6 * 48o = 36 * 6
55 * 112 - 55^2 * o = 216 * 6 + 6 * 48o
55 * 112 - 216 * 6 - 55^2 * o = 288o
55 * 112 - 216 * 6 = 288o + 55^2 * o
o = ((55 * 112 - 216 * 6) - 55^2 * o) / 288

Now, we can solve for o using the quadratic formula:
o = (-b ± √(b² - 4ac)) / 2a
o = (-(55^2) ± √((55^2)² - 4 * 1 * (55 * 112 - 216 * 6))) / (2 * 1)
o = (-(55^2) ± √(55^4 - 4 * 55 * 112 * 6 + 4 * (55 * 112 - 216 * 6)^2)) / 2

Now, we can find the two possible values for o and then solve for c using the expression we found earlier.

### Answer: The values of c and o that satisfy the given system of equations are not unique. There are two possible solutions: (c1, o1) and (c2, o2). To find the exact values, you can use the quadratic formula.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -7 and the second equation by 6 to make the coefficients of u in both equations the same:

-56w - 428u = -1190,
427w - 564u = 48.

Now, we can add both equations to eliminate u:

(427 - 564)w = 48 + 1190,
-98w = 1238,
w = -1238 / -98,
w = 12.58.

Now that we have the value of w, we can substitute it back into either equation to find the value of u. We'll use the first equation:

8w + 68u = 170,
8(12.58) + 68u = 170,
100.64 + 68u = 170,
68u = 170 - 100.64,
68u = 69.36,
u = 69.36 / 68,
u = 1.02.

### Answer: u = 1.02, w = 12.58.

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

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -38 and the second equation by 8 to make the coefficients of r the same in both equations:

-184*r - 24*f = -288
576*f + 294*r = 1456

Now, we'll add both equations to eliminate the variable f:

(576 - 184)*r = 1456 + 288
392*r = 1744

Finally, we'll solve for r:

r = 1744 / 392
r = 4.45 (rounded to two decimal places)

Now that we have the value of r, we can substitute it back into either equation to find the value of f. We'll use the first equation:

68*r + 8*f = 92
68*4.45 + 8*f = 92
299.6 + 8*f = 92
8*f = 92 - 299.6
8*f = -207.6
f = -207.6 / 8
f = -25.95 (rounded to two decimal places)

So, the solution to the system of equations is r = 4.45 and f = -25.95.

### Answer: The solution to the system of equations is r = 4.45 and f = -25.95.

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).

Mistral 7B:

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

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

1. 191d - 111r = 150
2. 78r - 42d = 32

Now, add the two equations:

191d - 111r + 78r - 42d = 150 + 32
(179d - 39r) = 182

Now, divide both sides by 179:

d - (39/179)r = 1 (182/179)

To find the values of d and r, we can use trial and error or solve the equation algebraically. Here, we will use trial and error.

Let's start by assuming that r = 10. Then, we can find the corresponding value of d:

d - (39/179) * 10 = 1 * (182/179)
d - 3.9 = 1
d = 4.9

Now, let's check if the value of r = 10 and d = 4.9 satisfy the original equations:

1. 67 * 4.9 - 37 * 10 = 324.3 - 370 = -45.7, which is not equal to 50.
2. 39 * 10 - 21 * 4.9 = 390 - 103.1 = 286.9, which is not equal to 16.

Since our initial assumption for r was incorrect, let's try another value for r, such as r = 11. Then, we can find the corresponding value of d:

d - (39/179) * 11 = 1 * (182/179)
d - 4.1 = 1
d = 5.1

Now, let's check if the value of r = 11 and d = 5.1 satisfy the original equations:

1. 67 * 5.1 - 37 * 11 = 335.7 - 397 = -61.3, which is not equal to 50.
2. 39 * 11 - 21 * 5.1 = 429 - 106.1 = 322.9, which is not equal to 16.

Since our second assumption for r was also incorrect, let's try another value for r, such as r = 12. Then, we can find the corresponding value of d:

d - (39/179) * 12 = 1 * (182/179)
d - 4.3 = 1
d = 5.3

Now, let's check if the value of r = 12 and d = 5.3 satisfy the original equations:

1. 67 * 5.3 - 37 * 12 = 351.1 - 444 = -92.9, which is not equal to 50.
2. 39 * 12 - 21 * 5.3 = 468 - 111.3 = 356.7, which is not equal to 16.

Since our third assumption for r was also incorrect, let's try another value for r, such as r = 13. Then, we can find the corresponding value of d:

d - (39/179) * 13 = 1 * (182/179)
d - 4.5 = 1
d = 5.5

Now, let's check if the value of r = 13 and d = 5.5 satisfy the original equations:

1. 67 * 5.5 - 37 * 13 = 363.5 - 481 = -117.5, which is not equal to 50.
2. 

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.

Mistral 7B:

 Reasoning: We can rearrange the first equation to isolate x: x = 163 / 50 - a.
We can rearrange the second equation to isolate x: x = 24 / 98 + 84a / 98.
Since x is the same in both equations, we can set the two expressions for x equal to each other:
(163 / 50 - a) = (24 / 98 + 84a / 98)

Solving this equation for a:

First, subtract 24/98 from both sides: (163 - 24a) / 50 = a / 98

Next, multiply both sides by 98 to eliminate the fraction: 163 - 24a = 98a

Now, add 24a to both sides: 163 = 122a

Finally, divide both sides by 122: a = 163 / 122

Now that we have the value of a, we can find the value of x using either equation. We'll use the first equation:
x = 163 / 50 - a = 163 / 50 - (163 / 122)

Cross-multiplying and simplifying:
x = (122 * 163 - 50 * 163) / (50 * 122) = 20666 / 6100

So, x = 20666 / 6100 ≈ 3.3823.

### Answer: x ≈ 3.3823, a ≈ 1.3483.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -44 and the second equation by 18 to make the coefficients of p in both equations the same:

-264 * p - 792 * b = -440
138 * b - 1464 * p = 948

Now, we'll add both equations to eliminate the variable b:

(-264 * p - 792 * b) + (138 * b - 1464 * p) = (-440) + 948
(-264 - 1464) * p = 138 * b + 508
-1728 * p = 138 * b + 508

Now, we'll divide both sides by 138 to isolate b:

p = (138 * b + 508) / -1728
p = (b + 3.75) / -12

Now, we can solve for b by setting p equal to a known value. Let's choose p = 1:

1 = (b + 3.75) / -12
12 * 1 = b + 3.75
12 = b + 3.75
b = 12 - 3.75
b = 8.25

Now that we have the value of b, we can find the value of p using the first equation:

67 * p + 18 * 8.25 = 110
67 * p = 110 - 148.5
67 * p = -38.5
p = -38.5 / 67
p = -0.5737

### Answer: p = -0.5737, b = 8.25

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.

Mistral 7B:

 Reasoning: Let's solve the first equation for c:
63c - 36e = 27
63c = 36e + 27
c = (36e + 27) / 63

Now, let's substitute this expression for c into the second equation:
8((36e + 27) / 63) + 32e = 69

Multiplying both sides by 63 to eliminate the fraction:
8(36e + 27) + 32e*63 = 69*63
288e + 216 + 2016e = 4187

Combining like terms:
2044e = 4187 - 216
2044e = 4001

Dividing both sides by 2044:
e = 4001 / 2044
e = 1.9595074626865673

Now, we can find the value of c using the expression we found earlier:
c = (36*1.9595074626865673 + 27) / 63
c = (69.59507462686567 + 27) / 63
c = 96.59507462686567 / 63
c = 1.5484375

### Answer: c = 1.5484375, e = 1.9595074626865673

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

Mistral 7B:

 Reasoning: To solve the system of linear equations, we can first multiply the first equation by -51 and the second equation by 26 to make the coefficients of p in both equations the same.

-1314 * x + 1459 * p = -531
1566 * x - 1459 * p = 1044

Now, we can add both equations to eliminate p:

(1566 - 1314) * x = 1044 + 531
252 * x = 1575

Finally, we can solve for x:

x = 1575 / 252
x = 6.25

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

26 * 6.25 + 29 * p = 107
156.25 + 29 * p = 107

Now, we can solve for p:

29 * p = 107 - 156.25
29 * p = -49.25

Finally, we can solve for p:

p = -49.25 / 29
p = -1.70

### Answer: x = 6.25, p = -1.70

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.

Mistral 7B:

  Reasoning: We can solve the system of equations by using the elimination method. First, we'll multiply the first equation by -10 and the second equation by 17 to make the coefficients of l in both equations the same.

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

(-290 * l) - (170 * g) + (17 * (31 * g)) - (17 * (10 * l)) = -680 + 289

(-290 * l) + (14 * g) = -391

Now, we can solve for g by multiplying both sides by 14/290:

g = (-391 * 14/290) / 14
g = -391/290 * 7/14
g = -7/10

Now that we have the value for g, we can substitute it back into the first equation to solve for l:

((29 * l) + (17 * (-7/10))) = 68

29l - 14.3 = 68

29l = 82.3

l = 82.3 / 29
l = 2.838

### Answer: g = -7/10, l = 2.838 (rounded to two decimal places)

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.

Mistral 7B:

 To find the values for a and c, we can first solve one of the equations for either a or c, and then use that equation to eliminate one variable in the other equation. Let's solve the first equation for c:

c = (20 + 54*a) / 33

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

24*a - 26*(20 + 54*a) / 33 = 29

Multiply both sides by 33 to eliminate the fraction:

792*a - 26*(20 + 54*a) = 887

Expand the right side:

792*a - 520 - 1364*a = 887

Combine like terms:

-632*a = 367

Divide both sides by -632:

a = -367 / 632

Now that we have the value for a, we can substitute it back into the equation we found for c:

c = (20 + 54*(-367/632)) / 33

Simplify the expression inside the parentheses:

c = (20 - 1884/632) / 33

Multiply both the numerator and denominator by 632:

c = (1260 - 1884) / 21168

Subtract 1260 from 1884:

c = -624 / 21168

Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 12:

c = -52 / 1766

### Answer: a = -367/632, c = -52/1766

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by -84 and the second equation by 71, and then add the two resulting equations to eliminate the variable 'd'.

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

6184d + (-672)j + 3087j - 5904d = -584448 + 6371

Combining like terms, we get:

(6184 + 3087)d + (3087 - 672)j = 6371 + 584448

10271d + 2415j = 58515

Now, we can solve for 'd' by dividing both sides by 10271:

d = (58515) / 10271

d = 5.71 (rounded to two decimal places)

Now that we have the value of 'd', we can substitute it back into either equation to find the value of 'j'. We'll use the first equation:

71(5.71) + 9j = 132

395.71 + 9j = 132

Subtracting 395.71 from both sides, we get:

9j = 132 - 395.71

j = (132 - 395.71) / 9

j = -24.97 (rounded to two decimal places)

### Answer: d = 5.71, j = -24.97

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.

Mistral 7B:

 Reasoning: We can solve this system of equations by using the elimination method. First, we'll multiply the first equation by -1 and add it to the second equation to eliminate the variable 'o'.

(-1 * (81 * o)) + (-1 * (26 * n)) + (87 * n) + (23 * o) = -163 + 143

This simplifies to:

-81o - 26n + 87n + 23o = 20

Combining like terms, we get:

61o + 61n = 20

Now, we can divide both sides by 61 to isolate 'o':

o = (20 - 61n) / 61

Since we don't have a specific value for 'n', we can't find the exact values for 'o'. However, we can express 'o' in terms of 'n':

o = (20 - 61n) / 61

### Answer: The values of o and n cannot be determined with the given information.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 61 and the second equation by -46, and then add the two resulting equations to eliminate the variable w:

(46 * s - 61 * w) * 61 + (-61 * s - 67 * w) * (-46) = 2 * 61 + 178 * (-46)

2766 * s - 3746 * w = -1262

Now, we'll multiply the first equation by -3746 and the second equation by 2766 and add them to eliminate the variable s:

(-2766 * s + 3746 * w) * (-3746) + (61 * s + 67 * w) * 2766 = -1262 * (-3746) + 178 * 2766

10144416 * w - 9803556 * s = 4644484

Now, we can solve for s:

s = (10144416 * w - 4644484) / 9803556

Now, we can substitute this expression for s into the first equation to solve for w:

46 * ((10144416 * w - 4644484) / 9803556) - 61 * w = 2

Multiplying both sides by 9803556 to eliminate the fraction:

46 * (10144416 * w - 4644484) - 61 * 9803556 * w = 19607104

Expanding and rearranging:

460288800 * w - 4644484 * 46 = 19607104

w = (19607104 + 4644484 * 46) / (460288800)

w = 4.000000000000003

Since w is a real number, we round it to 4.

Now, we can find s using the expression we found earlier:

s = (10144416 * 4 - 4644484) / 9803556

s = 3999999.999999999

Since s is not a real number, there is no solution to this system of equations with real numbers.

### Answer: There is no solution with real numbers.

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.

Mistral 7B:

 Reasoning: We can solve this system of equations by using the elimination method. First, we multiply the first equation by 3 and the second equation by 5 to eliminate the variable i:

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

Now, we add both equations:

153*k + 195*i + 195*i - 24*i = 258 + 965
350*i + 173*k = 1223

Now, we solve for i:

350*i = 1223 - 173*k
i = (1223 - 173*k) / 350

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

51*k - 8*(1223 - 173*k) / 350 = 86

Now, we multiply both sides by 350 to eliminate the fraction:

17351*k - 8*1223 + 136*173*k = 29900

Now, we gather like terms:

17351*k + 136*173*k = 29900 + 8*1223

Now, we solve for k:

17351*k + 25448*k = 30721

Now, we combine like terms:

42799*k = 30721

Now, we solve for k:

k = 30721 / 42799
k = 0.7154

Now, we substitute k back into the expression for i:

i = (1223 - 173*0.7154) / 350
i = (1223 - 122.39) / 350
i = 1100.61 / 350
i = 3.1443

### Answer: i = 3.1443, k = 0.7154

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

Mistral 7B:

 Reasoning: First, we can solve the first equation for l in terms of m:

l = 146 - 26m

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

93m + (146 - 26m) = 126

Solving for m:

93m + 146 - 26m = 126
67m = 22

m = 22 / 67

Since m is a fraction, we can't find an exact integer value for m. However, we can find the closest integer value by rounding m up to the nearest whole number:

m = 3

Now, substitute m = 3 into the expression for l:

l = 146 - 26(3) = 146 - 78 = 68

### Answer: The system of equations has no integer solutions, but the closest integer solution is m = 3 and l = 68.

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

Mistral 7B:

 Reasoning:

1) Rearrange the first equation to isolate one variable, say 'f':
(8 * f) = 66 - (39 * h)

2) Rearrange the second equation to isolate 'f':
(29 * f) = 119 - (46 * h)

Now we have two equations with one variable, 'f', that are equal to the same value. Set them equal to each other:

(8 * f) = (29 * f)

Solve for 'f':

8 = 29

This equation has no solution, so there is no valid pair of values for 'h' and 'f' that satisfy both equations.

### Answer: There is no valid pair of values for 'h' and 'f' that satisfy both equations.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we multiply the first equation by -69 and the second equation by 23, and then we add the two resulting equations:

(-69 * 22 * b) + (-69 * 23 * k) = -1438 + 1539 * k
(62 * k) - 69 * b = 14

Now, we can rearrange the first equation to isolate k:

1539 * k = 1438 + 69 * 22 * b
k = (1438 + 69 * 22 * b) / 1539

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

62 * ((1438 + 69 * 22 * b) / 1539) - 69 * b = 14

Now, we can solve for b:

948 * (1438 + 69 * 22 * b) - 69^2 * b^2 = 14 * 1539
1438 * 948 + 184672 * b - 69^2 * b^2 = 21583

Now, we can rearrange the equation to form a quadratic equation:

-69^2 * b^2 + 184672 * b - 1438 * 948 - 21583 = 0

Now, we can solve the quadratic equation using the quadratic formula:

b = (-184672 ± sqrt((184672)^2 - 4 * (-69^2 * (-1438 * 948 - 21583)))) / (2 * -69^2)

Now, we can calculate the values of b:

b1 = (-184672 + sqrt((184672)^2 - 4 * (-69^2 * (-1438 * 948 - 21583)))) / (2 * -69^2)
b2 = (-184672 - sqrt((184672)^2 - 4 * (-69^2 * (-1438 * 948 - 21583)))) / (2 * -69^2)

Now, we can substitute the values of b back into the equation for k:

k1 = (1438 + 69 * 22 * b1) / 1539
k2 = (1438 + 69 * 22 * b2) / 1539

Now, we can calculate the values of k:

k1 = (1438 + 69 * 22 * b1) / 1539
k2 = (1438 + 69 * 22 * b2) / 1539

Now, we can check if the solutions satisfy both equations:

22 * b1 + 23 * k1 = 109
62 * k1 - 69 * b1 = 14

22 * b2 + 23 * k2 = 109
62 * k2 - 69 * b2 = 14

If the solutions satisfy both equations, then we have found the correct values of k and b.

### Answer: The values of k and b that satisfy the given system of equations are k1 and b1, or k2 and b2, depending on which pair of solutions satisfy both 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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 2 and the second equation by 55 to make the coefficients of s the same in both equations:

1. 168m - 110s = 2
2. 3390m - 1100s = 4900

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

3390m - 168m - 110s + 110s = 4900 - 2
3322m = 4898

Now, we'll solve for m:

m = 4898 / 3322
m = 1.4721 (rounded to 4 decimal places)

Now that we have the value of m, we can substitute it back into either equation to solve for s. Let's use the first equation:

84(1.4721) - 55s = 1
120.4844 - 55s = 1
-55s = -120.4844 + 1
s = (120.4844 - 1) / -55
s = 2.1911 (rounded to 4 decimal places)

### Answer: m = 1.4721, s = 2.1911

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.

Mistral 7B:

 Reasoning: We can solve this system of equations by eliminating one variable. Let's eliminate 'b' by adding the two equations:

(6 * b) + (5 * k) + (95 * k) - (51 * b) = 105 + 67

Simplifying the equation:

(6 + 95) * k - (51) * b = 172

Now, we can see that the coefficient of 'b' is 0, so we have eliminated 'b'. We can solve for 'k':

(101) * k = 172

Dividing both sides by 101:

k = <<172/101=1.70392156862745>>1.7039 (rounded to 4 decimal places)

Now that we have the value of 'k', we can find the value of 'b' using the first equation:

(6 * b) + (5 * k) = 105

Substituting the value of 'k' we found:

(6 * b) + (5 * 1.7039) = 105

Solving for 'b':

6 * b = 105 - (5 * 1.7039)

6 * b = 105 - 8.5195

b = (105 - 8.5195) / 6

b = 16.8316 (rounded to 4 decimal places)

### Answer: b = 16.8316, k = 1.7039 (rounded to 4 decimal places)

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.

Mistral 7B:

 To solve the system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -1 and add it to the second equation to eliminate u:

(-1)*(33d + 62u) + (32u + 40d) = (-1)*114 + 83
-33d - 62u + 32u + 40d = -114 + 83
17d = 31

Now, we can solve for d:

d = 31 / 17
d = <<31/17=1.8235294117647059>>1.8235294117647059

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

33*(1.8235294117647059) + 62u = 114
61.39411764705883 + 62u = 114
62u = 114 - 61.39411764705883
62u = 52.60588235294117
u = 52.60588235294117 / 62
u = <<52.60588235294117/62=0.8524603174603175>>0.8524603174603175

### Answer: d = 1.8235294117647059, u = 0.8524603174603175

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

Mistral 7B:

 Reasoning: To solve this system of equations, we can first multiply the first equation by -67 and the second equation by 28 to make the coefficients of p equal in both equations.

-335 * c - 176 * p = -612
112 * c + 176 * p = 336

Now, we can add both equations to eliminate p:

(-335 * c - 176 * p) + (112 * c + 176 * p) = (-612) + 336
0 = 223 * c

Now, we can find the value of c:

c = 0 / 223
c = 0 (since division by zero is undefined)

However, since we have an inconsistent system of equations (i.e., no solution for c), we cannot find a unique solution for both c and p.

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

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -76 and the second equation by 12 to make the coefficients of r the same in both equations:

-396 * r - 84 * q = -522
-672 * q + 1032 * r = 912

Now, we'll add both equations to eliminate q:

(-396 * r - 84 * q) + (-672 * q + 1032 * r) = (-522) + 912
-1068 * q + 1428 * r = 390

Next, we'll solve for q:

1068 * q = 390 - 1428 * r
q = (390 - 1428 * r) / 1068

Now, we'll substitute this expression for q into the first equation to solve for r:

58 * r + 12 * ((390 - 1428 * r) / 1068) = 147

Multiplying both sides by 1068 to eliminate the fraction:

6204 * r + 12 * (390 - 1428 * r) = 147 * 1068

Expanding and simplifying:

6204 * r + 4680 - 17136 * r = 154088
-10932 * r = -107888

Dividing both sides by -10932:

r = 107888 / 10932
r = 9.999999999999999

Since r is a real number, we round it to the nearest integer:

r = 10

Now, we can find the value of q using the expression we found earlier:

q = (390 - 1428 * r) / 1068
q = (390 - 1428 * 10) / 1068
q = (390 - 14280) / 1068
q = -13380 / 1068
q = -12.5

### Answer: r = 10, q = -12.5

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.

Mistral 7B:

 To solve the system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 2 and the second equation by -3 to eliminate k:

94 * v - 6 * k = 20 (first equation multiplied by 2)
-219 * v - 6 * k = -384 (second equation multiplied by -3)

Now, we'll add the two equations:

(94 - 219) * v = 20 + 384
-125 * v = 404

To find v, we'll divide both sides by -125:

v = -404 / -125
v = 3.232 (rounded to four decimal places)

Now that we have the value of v, we can substitute it back into either equation to find k. We'll use the first equation:

47 * 3.232 - 3 * k = 10
144.844 - 3 * k = 10

To find k, we'll subtract 144.844 from both sides:

-3 * k = 10 - 144.844
-3 * k = -134.844

Finally, we'll divide both sides by -3:

k = -134.844 / -3
k = 44.948 (rounded to four decimal places)

### Answer: v = 3.232, k = 44.948

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?

Mistral 7B:

 Reasoning: First, we can solve the first equation for p:
89p - 41q = 60
89p = 60 + 41q
p = (60 + 41q) / 89

Now, we can substitute this expression for p into the second equation:
27((60 + 41q) / 89) + 91q = 124

Multiplying both sides by 89 to eliminate the fraction:
27(60 + 41q) + 91q \* 89 = 124 \* 89
1640 + 1807q + 7829q = 10864

Combining like terms:
9626q = -4264

Dividing both sides by 9626:
q = -4264 / 9626
q ≈ -0.4444

Now, we can find the value of p using the expression we found earlier:
p = (60 + 41q) / 89
p = (60 + 41 \* -0.4444) / 89
p ≈ 0.5556

### Answer: p ≈ 0.5556, q ≈ -0.4444

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

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by 3 and the second equation by 2 to make the coefficients of u the same in both equations:

3*(88*u) - 3*(96*d) = 3*12
6*(27*u) + 2*(36*d) = 2*71

Now, let's add both equations:

(3*88*u - 3*96*d) + (6*27*u + 2*36*d) = (3*12) + (2*71)

Simplifying the equation:

264*u - 288*d + 162*u + 72*d = 36 + 142

Combining like terms:

326*u + 50*d = 178

Now, let's isolate d:

50*d = 178 - 326*u
d = (178 - 326*u) / 50

Now, we can use the second equation to find another expression for d:

(27*u) + (36*d) = 71

Substitute the expression for d from the previous step:

(27*u) + (36*(178 - 326*u)) = 71

Simplifying the equation:

27*u + 6348 - 12176*u = 71

Combining like terms:

-11939*u + 6348 = 71

Now, let's isolate u:

11939*u = 6419
u = 6419 / 11939

Now, we can find the value of d using the expression we found earlier:

d = (178 - 326*u) / 50
d = (178 - 326*(6419/11939)) / 50

### Answer: u = 6419/11939, d = (178 - 326*(6419/11939)) / 50

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.

Mistral 7B:

  To solve the system of equations, we can first multiply the first equation by 2 and the second equation by 18 to make the coefficients of f equal in both equations:

40 * n - 36 * f = 18
3 * n - 2 * f = 70

Now, we can add both equations to eliminate f:

(40 * n - 36 * f) + (3 * n - 2 * f) = 18 + 70
43 * n - 34 * f = 88

Next, we can multiply the entire equation by 34/43 to make the coefficient of n equal to 1:

(43 * n - 34 * f) * (34/43) = 88 * (34/43)
n - (34 * f) * (1/43) = 88/43

Now, we can multiply both sides by 43 to get rid of the fraction:

n - f = 88

Finally, we can add f to both sides to solve for n:

n = f + 88

To find the value of f, we can substitute the value of n from the first equation into the second equation:

3 * (f + 88) - 2 * f = 70
3 * f + 264 - 2 * f = 70
f = 70 - 264 / 3
f = 70 - 88/3
f = 70 - 29.33 (approximately)

Since f cannot be a negative number, we can round up to the nearest whole number:

f = 41

Now, we can find the value of n:

n = f + 88
n = 41 + 88
n = 129

### Answer: f = 41, n = 129.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -37 and the second equation by 9 to make the coefficients of j equal in both equations:

-241 * l - 291 * j = -399
-198 * j - 189 * l = -642

Now, we'll add both equations to eliminate j:

(-241 * l - 291 * j) + (-198 * j - 189 * l) = (-399) + (-642)
-439 * l = -1041

Now, we'll solve for l:

l = 1041 / -439
l = -2.36 (rounded to two decimal places)

Now that we have the value of l, we can substitute it back into the first equation to find the value of j:

7 * l + 97 * j = 133
7 * (-2.36) + 97 * j = 133
-16.52 + 97 * j = 133
97 * j = 149.48
j = 149.48 / 97
j = 1.55 (rounded to two decimal places)

### Answer: j = 1.55, l = -2.36 (rounded to two decimal places)

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.

Mistral 7B:

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

84(21d - 46f) = 4 * 53
24(8d + 84f) = 3 * 133

Now, we can eliminate d by adding the two equations:

(1712d - 1004f) + (192d + 2520f) = 212 * 53 + 399 * 133
1934d + 3524f = 110193

Now, we can solve for d:

1934d = 110193 - 3524f
d = (110193 - 3524f) / 1934

Now, let's substitute this expression for d back into the first equation to solve for f:

21((110193 - 3524f) / 1934) - 46f = 53

Multiply both sides by 1934 to clear the fraction:

220793 - 71846f - 46f * 1934 = 53 * 1934

Now, let's combine like terms:

220747f = 1158661

Finally, divide both sides by 220747 to solve for f:

f = 1158661 / 220747

Now, we can find the value of d using the expression we found earlier:

d = (110193 - 3524f) / 1934
d = (110193 - 3524 * (1158661 / 220747)) / 1934

### Answer: d = 105.64, f = 5.24 (rounded to two decimal places)

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, we'll multiply the first equation by -1 and add it to the second equation to eliminate w:

(-1 * 74u - 11w) + (66u - 68w) = (-1 * 116) + 21
-148u + 11w = -135

Now, we'll solve for u:

148u = 135 + 11w
u = (135 + 11w) / 148

Next, we'll substitute this expression for u back into the first equation to solve for w:

74((135 + 11w) / 148) + 11w = 116

Multiplying both sides by 148 to eliminate the fraction:

10,495 + 1,574w + 11w = 19,648
1,585w = 9,153

Now, we'll solve for w:

w = 9,153 / 1,585
w = 5,783 / 79
w = 72 (approximately)

Now that we have the value of w, we can find the value of u:

u = (135 + 11 * 72) / 148
u = (135 + 864) / 148
u = 999 / 148
u = 6.71 (approximately)

### Answer: u = 6.71 (approximately), w = 72 (approximately)

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 47 and the second equation by -42 to make the coefficients of j equal in both equations:

47 * (76 * f - 42 * j) = 47 * 96
-42 * (47 * j + 34 * f) = -42 * 136

Multiplying both sides of the first equation:
3342 * f - 2002 * j = 4168

Multiplying both sides of the second equation:
-1864 * j - 1456 * f = -5544

Now, we'll add both equations to eliminate j:
(3342 * f - 2002 * j) + (-1864 * j - 1456 * f) = 4168 + (-5544)
(3342 - 1864) * f = 4168 + 5544
1478 * f = 9712

Now, we'll solve for f:
f = 9712 / 1478
f = 6.583333333333333

Now that we have the value of f, we can substitute it back into the first equation to find the value of j:
76 * 6.583333333333333 - 42 * j = 96
461.8666666666666 - 42 * j = 96
-42 * j = 96 - 461.8666666666666
-42 * j = -365.8666666666666
j = -365.8666666666666 / -42
j = 8.714772727272727

### Answer: f = 6.583333333333333, j = 8.714772727272727

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.

Mistral 7B:

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

(-68u - 32e) + (63e - 69u) = 174 + 1
-1e = 176

Now, let's solve for e:

e = -176

Now that we have the value of e, we can substitute it back into the first equation to solve for u:

68u + 32(-176) = 174
68u = 174 + 5648
68u = 5822

Now, let's solve for u:

u = 5822 / 68
u = 85.58823529411765

Since u is a variable representing a number of units, we can round it to the nearest whole number:

u = 86

### Answer: u = 86, e = -176.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by 3 and the second equation by 2 to make the coefficients of n equal in both equations:

171p + 12n = 387
48p + 78n = 308

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

(48p - 171p) + (78n - 12n) = 308 - 387
-123p + 66n = -79

Next, we'll solve for p:

-123p = -79 - 66n
p = (79 + 66n) / 123

Now, we'll substitute this expression for p into the first equation:

57((79 + 66n) / 123) + 4n = 129

Multiplying both sides by 123 to eliminate the fraction:

4183 + 3802n + 574n = 16383

Combining like terms:

9546n = 12190

Now, we'll solve for n:

n = 12190 / 9546
n ≈ 1.2714

Since n is not a whole number, there are no integer solutions for p and n that satisfy the given system of linear equations.
### Answer: There are no integer solutions for p and n that satisfy the given system of linear equations.

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by 14 and the second equation by 44 to make the coefficients of y the same in both equations:

99 * z - 592 * y = 448
264 * y + 599 * z = 4928

Now, let's add both equations:

(99 + 264) * z = (448 + 4928)
363 * z = 5376

Now, let's solve for z:

z = 5376 / 363
z = <<5376/363=14.814814814814814>>14.814814814814814

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

66 * z - 44 * y = 32
66 * 14.814814814814814 - 44 * y = 32
936.6844814814814 - 44 * y = 32

Now, let's solve for y:

44 * y = 936.6844814814814 - 32
y = (936.6844814814814 - 32) / 44
y = 21.33272727272727

### Answer: y = 21.33272727272727, z = 14.814814814814814

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 11 and the second equation by 58 to make the coefficients of t the same in both equations:

1. (83 * t - 58 * h) * 11 = 45 * 11
899 * t - 636 * h = 495

2. (69 * h + 11 * t) * 58 = 124 * 58
3942 * h + 660 * t = 7136

Now, let's add both equations to eliminate h:

(899 * t - 636 * h) * 11 + (3942 * h + 660 * t) * 58 = 495 * 11 + 7136 * 58
10667 * t + 23576 * h = 128311

Next, let's solve for h:

23576 * h = 128311 - 10667 * t
h = (128311 - 10667 * t) / 23576

Now, we can substitute this expression for h into the first equation to solve for t:

83 * t - 58 * ((128311 - 10667 * t) / 23576) = 45

Multiplying both sides by 23576 to eliminate the fraction:

193488 * t - 58 * (128311 - 10667 * t) = 1077120

Expanding and simplifying:

193488 * t - 7346676 + 58 * 10667 * t = 1077120
193488 * t + 58 * 10667 * t - 7346676 = -1077120
(193488 + 58 * 10667) * t = 7346676 + 1077120
2061556 * t = 7453796

Finally, let's solve for t:

t = 7453796 / 2061556
t = 3.625

Now, we can find h using the expression we found earlier:

h = (128311 - 10667 * t) / 23576
h = (128311 - 10667 * 3.625) / 23576
h = 0.4375

### Answer: t = 3.625, h = 0.4375

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?

Mistral 7B:

  Reasoning: We can solve the system of equations by setting the expressions for h equal to each other and the expressions for o equal to each other.

(79 * h) - (61 * o) = (16 * h) - (12 * o)

79h - 61o = 16h - 12o

57h - 49o = 0

(57 * o) = (49 * h)

o = (49/57) * h

Now, we can set the expressions for h equal to each other:

(79 * h) - (61 * o) = (16 * h) - (12 * o)

(79 - 16) * h = (61 - 12) * (49/57) * h

63 * h = 49 * 61 / 57 * h

63 = 49 * 61 / 57

Multiplying both sides by 57, we get:

3641 = 3038

This equation is not true, so there is no solution for this system of equations.
### Answer: There is no solution for this system of equations.

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

Mistral 7B:

 Reasoning: To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -90 and the second equation by 56 to make the coefficients of s in both equations the same.

-360 * y - 4800 * s = -396
3280 * y - 5160 * s = 960

Now, we'll add both equations to eliminate s:

(-360 * y - 4800 * s) + (3280 * y - 5160 * s) = (-396) + 960
(-840 * y) = 564

Now, we'll solve for y:

y = 564 / -840
y = -0.6666666666666667

Now that we have the value for y, we can substitute it back into either equation to solve for s. We'll use the first equation:

4 * (-0.6666666666666667) + 56 * s = 139
-2.666666666666667 + 56 * s = 139
53.33333333333333 * s = 141.6666666666667
s = 141.6666666666667 / 53.33333333333333
s = 2.666666666666667

### Answer: s = 2.666666666666667, y = -0.6666666666666667

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.

Mistral 7B:

 To solve the pair of simultaneous equations, we can use the elimination method. First, we'll multiply the first equation by 5 and the second equation by 3 to eliminate z:

210 * d - 20 * z = 375
120 * d + 135 * z = 486

Now, we'll add both equations:

(210 * d + 120 * d) - (20 * z + 135 * z) = 375 + 486
330 * d - 155 * z = 861

Next, we'll solve for z:

z = (861 - 330 * d) / (-155)

Now, we'll substitute this expression for z into the first equation:

42 * d - 4 * ((861 - 330 * d) / (-155)) = 75

Multiply both sides by -155 to get rid of the fraction:

-6330 * d + 4 * (861 - 330 * d) = -11795

Expand and simplify:

-6330 * d + 3444 - 1320 * d = -11795
-7654 * d = -16249

Now, divide both sides by -7654:

d = 16249 / 7654

Since d is a fraction, we'll simplify it:

d = 22 / 11

Now, we can find the value of z using the expression we found earlier:

z = (861 - 330 * (22/11)) / (-155)
z = (861 - 722) / (-155)
z = 139 / 155

Since z is a fraction, we'll simplify it:

z = 13/15

### Answer: d = 22/11, z = 13/15

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.

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, we'll multiply the first equation by -1 to eliminate 'a':

(-1 * (42 * o)) + (-1 * (24 * a)) = -1 * 142
-42 * o - 24 * a = -142

Now, we'll add the modified first equation to the second equation:

(-42 * o - 24 * a) + (42 * a + 6 * o) = -142 + 75
-24 * a = -67

Now, we'll solve for 'a':

a = -67 / -24
a = 2.7916666666666665

Now, we can substitute the value of 'a' back into the first equation to solve for 'o':

(42 * o) + (24 * 2.7916666666666665) = 142
42 * o = 142 - 66.24
42 * o = 75.76

Now, we'll solve for 'o':

o = 75.76 / 42
o = 1.8033333333333334

### Answer: a = 2.7916666666666665, o = 1.8033333333333334

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.

Mistral 7B:

  To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 8 and the second equation by 3 to make the coefficients of r equal in both equations:

3*39*r - 2*3*p = 36*3 (first equation)
4*16*p - 3*84*r = 36*4 (second equation)

Now, let's add both equations:

(3*39 + 4*16)*r - (2*3 + 3*84)*p = 36*3 + 36*4
133*r - 258*p = 252

Next, let's multiply the entire equation by 1/258 to make the coefficient of p equal to 1:

133*r/258 - 258*p/258 = 252/258
r/2 - p = 252/258

Now, let's multiply the entire equation by 258 to eliminate the fraction:

r - 258*p = 516

Finally, let's solve for p:

p = (r - 516)/258

Now, we can use substitution to find the value of r. Let's choose a value for r and solve for p. For example, let's try r = 10:

p = (10 - 516)/258
p = -195/258

Now, we can check if this value of p satisfies the original equations:

39*(-195/258) - 2*p = 45
39*(-195/258) + 380/258 = 45
(39*-195 + 380)*1/258 = 45*258
-7230 + 380 = 117600/258
-7230 + 380 = 452
-6850 = 452

Since this is not true, the solution we found is incorrect. Let's try another value for r, such as r = 11:

p = (11 - 516)/258
p = -495/258

Now, let's check if this value of p satisfies the original equations:

39*(-495/258) - 2*p = 45
39*(-495/258) + 990/258 = 45
(-17645 + 990)*1/258 = 45*258
-16655 = 117600/258
-16655 = 452

Since this is not true, the solution we found is incorrect. Let's try another value for r, such as r = 12:

p = (12 - 516)/258
p = -484/258

Now, let's check if this value of p satisfies the original equations:

39*(-484/258) - 2*p = 45
39*(-484/258) + 968/258 = 45
(-17516 + 968)*1/258 = 45*258
-16548 = 117600/258
-16548 = 452

Since this is not true, the solution we found is incorrect. Let's try another value for r, such as r = 13:

p = (13 - 516)/258
p = -473/258

Now, let's check if this value of p satisfies the original equations:

39*(-473/258) - 2*p = 45
39*(-473/258) + 9

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

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 8 and the second equation by 52 to make the coefficients of 'd' the same in both equations:

1. (168 * d) - (416 * w) = 56
2. (3280 * w) - (416 * d) = 2940

Now, let's add both equations to eliminate 'd':

(168 * d) - (416 * w) + (3280 * w) - (416 * d) = 56 + 2940
(168 + 3280) * w = 2996
2448 * w = 2996

Now, let's solve for 'w':

w = 2996 / 2448
w = 1.225

Now that we have the value of 'w', we can find the value of 'd' using either equation. Let's use the first equation:

(23 * d) - (52 * 1.225) = 7
23d - 63.3 = 7
23d = 70.3

Now, let's solve for 'd':

d = 70.3 / 23
d = 3.057

### Answer: d = 3.057, w = 1.225

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by -52 and the second equation by 71 to make the coefficients of z the same in both equations:

-362 * z - 3120 * n = -928
-362 * z + 4937 * n = 1327

Now, add both equations:

(-3120 * n) + (4937 * n) = -928 + 1327
1817 * n = 400

Now, divide by 1817 to find the value of n:

n = <<400/1817=0.21999999999999998>>0.22 (approximately)

Now, substitute the value of n back into the first equation to find the value of z:

(71 * z) + (60 * 0.22) = 184
71 * z = 184 - 13.2
71 * z = 170.8
z = <<170.8/71=2.411111111111111>>2.41 (approximately)

### Answer: The values of n and z are approximately 0.22 and 2.41, respectively.

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

Mistral 7B:

 To solve this system of linear equations, we can use the elimination method. First, let's multiply the first equation by -84 and the second equation by 70 to make the coefficients of e in both equations the same:

-5670 * e - 6360 * z = -14560
-6430 * z + 5670 * e = 14000

Now, let's add both equations:

(-5670 - 6430) * e + (-6360 - (-6360)) * z = -14560 + 14000
-12000 * e + 0 * z = 440

Now, divide by -12000:

e = -440 / -12000

e = 36.666666666666664

Now, let's substitute e = 36.666666666666664 into the first equation:

70 * 36.666666666666664 + 90 * z = 189
2560.3999999999998 + 90 * z = 189

Now, let's subtract 2560.3999999999998 from both sides:

90 * z = 189 - 2560.3999999999998
90 * z = -2371.3999999999998

Now, let's divide by 90:

z = -2371.3999999999998 / 90
z = -26.346666666666665

### Answer: e = 36.666666666666664, z = -26.346666666666665

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 11 and the second equation by 44:

1) 26o - 44f = 95
(11 * (26o - 44f)) = (11 * 95)
261o - 494f = 1045

2) 87f + 11o = 169
(44 * (87f + 11o)) = (44 * 169)
3884f + 484o = 7382

Now, let's add the two modified equations:

(261o - 494f) + (3884f + 484o) = 1045 + 7382
261o + 3884f + 484o - 494f = 8427

Combining like terms:
261o + 3378f = 8427

Now, let's isolate one of the variables. We'll solve for o:

261o = 8427 - 3378f
o = (8427 - 3378f) / 261

Now, we can substitute this expression for o into the first equation to solve for f:

26((8427 - 3378f) / 261) - 44f = 95
8427 - 683f - 44f = 26 * 95 * 261
8427 - 683f - 44f = 544446

Now, let's isolate f:

683f + 44f = 8427 - 544446
727f = -43619

Finally, let's solve for f:

f = -43619 / 727
f ≈ -60.14 (rounded to two decimal places)

Now that we have the value for f, we can find the value for o using the expression we found earlier:

o = (8427 - 3378f) / 261
o = (8427 - 3378 * -60.14) / 261
o ≈ 114.68 (rounded to two decimal places)

So, the solution to the system of equations is o ≈ 114.68 and f ≈ -60.14.

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 5 and the second equation by 2:

200*z - 100*p = 255
12*z + 116*p = 330

Now, let's add both equations:

(200*z - 100*p) + (12*z + 116*p) = 255 + 330
212*z - 96*p = 585

Next, let's multiply the first equation by 96 and the second equation by 10:

200*z - 100*p = 255
2120*z - 960*p = 5850

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

(2120*z - 200*z) - (960*p - 100*p) = 5850 - 255
2020*z = 5600

Finally, let's solve for z:

z = 5600 / 2020
z = 2.772727272727273

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

40*z - 20*p = 51
40*2.772727272727273 - 20*p = 51
110.9090909090909 - 20*p = 51

Now, let's solve for p:

20*p = 51 - 110.9090909090909
20*p = -59.9090909090909
p = -59.9090909090909 / 20
p = -2.995454545454545

### Answer: z = 2.772727272727273, p = -2.995454545454545

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.

Mistral 7B:

 To solve this system of equations, we can use the elimination method. First, let's multiply the first equation by 3 and the second equation by 89 to make the coefficients of f the same in both equations:

213s - 267f = 15
2703f + 890s = 7447

Now, let's add both equations to eliminate f:

(213s + 2703f) + (-267f + 890s) = 15 + 7447
(213s + 2703f) + (890s - 267f) = 7462

Combining the terms with s gives us:

3003s = 7462

Now, let's solve for s:

s = 7462 / 3003
s = 2.4814 (rounded to 4 decimal places)

Now that we have the value of s, we can find the value of f using either of the original equations. Let's use the first equation:

(71 * 2.4814) - (89 * f) = 5
173.7001 - 89f = 5

Now, let's solve for f:

89f = 168.7001
f = 168.7001 / 89
f = 1.8922 (rounded to 4 decimal places)

### Answer: s = 2.4814, f = 1.8922

Expected answer: {f: 6553/1103, s: 8292/1103}

Correct? No