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

Qwen2-Math 7B:

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

First, we can multiply the second equation by 40/30 to make the coefficients of s the same:

(40/30) * (30 * s) + (40/30) * (12 * q) = (40/30) * 121

This simplifies to:

40 * s + (160/30) * q = (40/30) * 121

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

(40 * s + (160/30) * q) - ((40 * s) - (91 * q)) = (40/30) * 121 - 37

This simplifies to:

(160/30 + 91) * q = (40/30) * 121 - 37

Now, we can solve for q:

q = ((40/30) * 121 - 37) / (160/30 + 91)

Once we have the value of q, we can substitute it back into one of the original equations to find the value of s.

### Answer: q = <<(40/30) * 121 - 37) / (160/30 + 91)>>, s = <<(40 * q - 37) / 91>>

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 6 and the second equation by 4 to make the coefficients of b the same:
24 * b + 264 * m = 1080
316 * m - 24 * b = 192
Now, we can add the two equations to eliminate b:
264 * m + 316 * m = 1080 + 192
580 * m = 1272
m = 1272 / 580 = <<1272/580=2.19>>2.19
Now, we can substitute the value of m into one of the original equations to solve for b:
4 * b + 44 * 2.19 = 180
4 * b + 96.36 = 180
4 * b = 180 - 96.36 = <<180-96.36=83.64>>83.64
b = 83.64 / 4 = <<83.64/4=20.91>>20.91
### Answer: b = 20.91, m = 2.19

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

Correct? No

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

Qwen2-Math 7B:

 Reasoning: 
First, we can solve the first equation for o: 
42 * o = 28 + 15 * g 
o = (28 + 15 * g) / 42 
Next, we can substitute this expression for o into the second equation: 
47 * ((28 + 15 * g) / 42) + 29 * g = 141 
Simplifying this equation, we get: 
(47 * 28 + 47 * 15 * g) / 42 + 29 * g = 141 
Multiplying both sides by 42, we get: 
47 * 28 + 47 * 15 * g + 29 * 42 * g = 141 * 42 
Simplifying this equation, we get: 
1316 + 705 * g + 1218 * g = 5922 
Combining like terms, we get: 
1923 * g = 4606 
Dividing both sides by 1923, we get: 
g = 4606 / 1923 
g = <<4606/1923=2.4>><<2.4>> 
Substituting this value of g back into the expression for o, we get: 
o = (28 + 15 * 2.4) / 42 
o = (28 + 36) / 42 
o = 64 / 42 
o = <<64/42=1.52>> 
Therefore, the solution to the system of equations is o = <<1.52>>1.52 and g = <<2.4>>2.4.
### Answer: o = 1.52, g = 2.4

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use elimination. Multiply the first equation by 76 and the second equation by 12 to eliminate v:
(76 * ((12 * v) - (6 * o))) = 76 * 21
(12 * ((76 * v) - (45 * o))) = 12 * 50
This simplifies to:
(912 * v) - (456 * o) = 1596
(912 * v) - (540 * o) = 600
Subtract the second equation from the first to eliminate v:
(912 * v) - (456 * o) - ((912 * v) - (540 * o)) = 1596 - 600
This simplifies to:
84 * o = 996
Divide both sides by 84 to solve for o:
o = <<84/996=12>>12
Substitute o = 12 into the first equation to solve for v:
((12 * v) - (6 * 12)) = 21
(12 * v) - 72 = 21
Add 72 to both sides:
(12 * v) = 93
Divide both sides by 12 to solve for v:
v = <<93/12=7.75>>7.75
### Answer: v = 7.75, o = 12

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 2 and the second equation by 75 to make the coefficients of f the same:
150 * f + 50 * g = 276
150 * f + 6750 * g = 10725
Now, we can subtract the first equation from the second equation to eliminate f:
6700 * g = 10449
g = <<10449/6700=1.55>>1.55
Now, we can substitute the value of g back into one of the original equations to find the value of f:
75 * f + 25 * 1.55 = 138
75 * f = 138 - 38.75
f = <<(138-38.75)/75=1.32>>1.32
### Answer: f = 1.32, g = 1.55

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination method.
Let's use the elimination method.
First, we can multiply the second equation by 4 to make the coefficients of y equal:
4 * (7 = 65 * n - 79 * y) => 28 = 260 * n - 316 * y
Now, we can add the two equations to eliminate y:
194 + 28 = 4 * y + 14 * n + 260 * n - 316 * y
222 = 274 * n - 312 * y
Now, we can solve for n:
222 = 274 * n => n = 222 / 274 => n = <<222/274=0.81>>0.81
Now, we can substitute the value of n back into one of the original equations to solve for y:
194 = 4 * y + 14 * 0.81 => 194 = 4 * y + 11.34 => 4 * y = 194 - 11.34 => 4 * y = 182.66 => y = 182.66 / 4 => y = <<182.66/4=45.665>>45.665
### Answer: y = 45.665, n = 0.81

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From the second equation, we can express l in terms of g: l = (6 + 53 * g) / 41.
Substituting this expression for l into the first equation, we get: 146 = 28 * g + 26 * ((6 + 53 * g) / 41).
Solving for g, we get: g = <<146 - 26 * (6 + 53 * g) / 41>>.
Substituting this value of g back into the expression for l, we get: l = <<(6 + 53 * g) / 41>>.
Therefore, the values of l and g that satisfy the two equations are l = <<(6 + 53 * g) / 41>> and g = <<146 - 26 * (6 + 53 * g) / 41>>.
### Answer: l = <<(6 + 53 * g) / 41>>, g = <<146 - 26 * (6 + 53 * g) / 41>>

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.

Qwen2-Math 7B:

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

First, we can multiply the first equation by 7 and the second equation by 56 to make the coefficients of y the same:

1) 140 * p + 392 * y = 630
2) 4876 * p + 392 * y = 5488

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

4876 * p - 140 * p = 5488 - 630
4736 * p = 4858

Now, we can solve for p:

p = 4858 / 4736
p = <<4858/4736=1.0258>>1.0258

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

20 * 1.0258 + 56 * y = 90
20.516 + 56 * y = 90
56 * y = 90 - 20.516
56 * y = 69.484

Now, we can solve for y:

y = 69.484 / 56
y = <<69.484/56=1.2404>>1.2404

Therefore, the solution to the system of equations is p = 1.0258 and y = 1.2404.

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the second equation by 11 to make the coefficients of k the same: 72*k - 22*d = 17 and 756*d + 759*k = 1056.
Next, we can subtract the first equation from the second equation to eliminate k: 756*d + 759*k - (72*k - 22*d) = 1056 - 17, which simplifies to 734*d = 1039.
Finally, we can solve for d: d = 1039/734 = <<1039/734=1.41>>1.41.
Substituting d = 1.41 into the first equation, we get 72*k - 22*1.41 = 17, which simplifies to 72*k = 17 + 31.02 = 48.02.
Solving for k, we get k = 48.02/72 = <<48.02/72=0.67>>0.67.
### Answer: k = 0.67, d = 1.41

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

Qwen2-Math 7B:

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

First, we can multiply the first equation by 10 and the second equation by 73 to make the coefficients of h the same:

730 * h - 330 * d = 480

730 * d + 1022 * h = 6593

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

730 * d + 1022 * h - (730 * h - 330 * d) = 6593 - 480

730 * d + 1022 * h - 730 * h + 330 * d = 6113

1060 * d = 6113

d = 6113 / 1060

d = <<6113/1060=5.77>>5.77

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

73 * h - 33 * 5.77 = 48

73 * h - 190.41 = 48

73 * h = 238.41

h = 238.41 / 73

h = <<238.41/73=3.26>>3.26

### Answer: d = <<6113/1060=5.77>>5.77, h = <<238.41/73=3.26>>3.26

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

Qwen2-Math 7B:

 Reasoning: 
From equation 1, we can express q in terms of e: q = (29 + 44 * e) / 43.
Substituting this expression for q in equation 2, we get: 30 * ((29 + 44 * e) / 43) + 43 * e = 130.
Simplifying this equation, we get: 290 + 1320 * e + 1809 * e = 5590.
Combining like terms, we get: 3129 * e = 5300.
Dividing both sides by 3129, we get: e = 5300 / 3129.
Substituting this value of e back into the expression for q, we get: q = (29 + 44 * (5300 / 3129)) / 43.
Simplifying this expression, we get: q = (29 + 73200 / 3129) / 43.
Simplifying further, we get: q = (29 * 3129 + 73200) / (43 * 3129).
Simplifying this expression, we get: q = (89741 + 73200) / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 134547.
Simplifying further, we get: q = 162941 / 134547.
Simplifying this expression, we get: q = 162941 / 13

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))

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From the first equation, we can express r in terms of a: r = (53 + 74 * a) / 89.
Substituting this expression for r in the second equation, we get: 109 = ((37 * a) + (6 * ((53 + 74 * a) / 89))).
Simplifying this equation, we get: 109 = (37 * a) + (6 * (53 + 74 * a) / 89).
Multiplying both sides by 89, we get: 9681 = (37 * a) * 89 + (6 * (53 + 74 * a)).
Expanding and simplifying, we get: 9681 = 3293 * a + 318 + 444 * a.
Combining like terms, we get: 9681 = 3737 * a + 318.
Subtracting 318 from both sides, we get: 9363 = 3737 * a.
Dividing both sides by 3737, we get: a = 9363 / 3737 = <<9363/3737=2.504>>2.504.
Substituting this value of a back into the expression for r, we get: r = (53 + 74 * 2.504) / 89 = <<(53 + 74 * 2.504) / 89=2.504>>2.504.
### Answer: r = 2.504, a = 2.504

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.

Qwen2-Math 7B:

 Reasoning: Let's solve the system of equations step by step.

From the first equation, we have:
42g + 12q = 169

From the second equation, we have:
12q - 50g = 19

We can solve this system using substitution or elimination. Let's use elimination. Multiply the second equation by 42/50 to align the coefficients of 'g':
(42/50) * (12q - 50g) = (42/50) * 19
(42/50) * 12q - (42/50) * 50g = (42/50) * 19
(252/50)q - 42g = (798/50)

Now, add this to the first equation to eliminate 'g':
42g + 12q + (252/50)q - 42g = 169 + (798/50)
12q + (252/50)q = 169 + (798/50)
(600/50)q + (252/50)q = (8450/50) + (798/50)
(852/50)q = (9248/50)
q = (9248/50) / (852/50)
q = 9248 / 852
q = <<9248/852=10.84>>10.84

Now, substitute the value of 'q' back into one of the original equations to solve for 'g':
42g + 12 * 10.84 = 169
42g + 129.68 = 169
42g = 169 - 129.68
42g = 39.32
g = 39.32 / 42
g = <<39.32/42=0.936>>0.936

### Answer: g = 0.936 kg, q = 10.84 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

Qwen2-Math 7B:

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

First, we can multiply the first equation by 2 to make the coefficients of s the same:

74 * s - 22 * v = 108

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

(74 * s - 22 * v) - (82 * s - 62 * v) = 108 - 41

This simplifies to:

-8 * s + 40 * v = 67

Now, we can solve for v:

v = (67 + 8 * s) / 40

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

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

Solving this equation for s, we get:

s = <<37 * s - 11 * ((67 + 8 * s) / 40) = 54|solve for s|>>1.5

Substituting this value of s back into the expression for v, we get:

v = (67 + 8 * 1.5) / 40 = <<(67 + 8 * 1.5) / 40|calculate v|>>2.5

### Answer: s = 1.5, v = 2.5

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

Correct? No

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use elimination. Multiply the first equation by 48 and the second equation by 41 to eliminate c:

1968 * z = 7248
3198 * z = 1968

Subtract the second equation from the first:

-1230 * z = -1230

Divide both sides by -1230:

z = 1

Substitute z = 1 into the first equation:

41 * c + 65 * 1 = 151

Solve for c:

41 * c = 86

c = 86 / 41

c = 2

### Answer: c = 2, z = 1

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?

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From the first equation, we can express c in terms of i:

c = (7 + 91 * i) / 60

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

7 * i + 76 * ((7 + 91 * i) / 60) = 148

Simplifying this equation, we get:

i = <<7 * i + 76 * ((7 + 91 * i) / 60) = 148; i = 2;>>2

Substituting this value of i back into the expression for c, we get:

c = (7 + 91 * 2) / 60 = <<(7 + 91 * 2) / 60 = 3;>>3

Therefore, the values of c and i are 3 and 2, respectively.
### Answer: c = 3, i = 2

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of linear equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 41 and the second equation by 37 to make the coefficients of e the same:
1) 2911*v - 1517*e = 2819
2) 1519*e + 2812*v = 6812
Now, we can add the two equations to eliminate e:
2911*v + 2812*v = 2819 + 6812
5723*v = 9631
v = <<5723/9631=0.593>>0.593
Now, we can substitute the value of v into one of the original equations to find e:
71*0.593 - 37*e = 69
42.403 - 37*e = 69
-37*e = 26.597
e = <<26.597/-37=-0.719>>-0.719
### Answer: e = -0.719, v = 0.593

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution. From the first equation, we can express 'v' in terms of 'd': v = (113 - 69d)/25. Substituting this expression into the second equation, we get: 26d + 42((113 - 69d)/25) = 85. Solving this equation for 'd', we get: d = <<26d + 42((113 - 69d)/25) = 85, solve for d>>0.5. Substituting this value of 'd' back into the expression for 'v', we get: v = <<v = (113 - 69d)/25, substitute d = 0.5>>0.5.
### Answer: d = 0.5, v = 0.5

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

Qwen2-Math 7B:

 Reasoning: 
43 * z - 91 * g = 33
72 * g - 3 * z = 68

Solving the system of equations, we get:
g = <<43z-91g=33,72g-3z=68|10>>
z = <<43z-91g=33,72g-3z=68|11>>

### Answer: g = 10, z = 11

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.

Qwen2-Math 7B:

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

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

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

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

1482c = 2340

Divide both sides by 1482 to find c:

c = <<1482/2340=0.632>>0.632

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

50(0.632) + 12f = 92
31.6 + 12f = 92
12f = 60.4
f = <<60.4/12=5.033>>5.033

Therefore, the quantity of cherries (c) is approximately 0.632 and the quantity of figs (f) is approximately 5.033.
### Answer: c = 0.632, f = 5.033

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From equation 1, we can express u in terms of d: u = (7 + 75d)/87.
Substitute this expression for u in equation 2: 85d - 82((7 + 75d)/87) = 54.
Solving for d, we get d = <<82/3>>27.33.
Substitute this value of d back into the expression for u: u = (7 + 75(27.33))/87 = <<82/3>>27.33.
### Answer: u = <<82/3>>27.33, d = <<82/3>>27.33

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?

Qwen2-Math 7B:

 Reasoning: We have two equations:
(75 * a) - (4 * i) = 42
(10 * i) + (13 * a) = 160
We can solve this system of equations using substitution or elimination method.
Let's use the elimination method.
First, we can multiply the first equation by 10 and the second equation by 75 to make the coefficients of a equal:
(750 * a) - (40 * i) = 420
(750 * i) + (975 * a) = 12000
Now, we can add the two equations to eliminate a:
(750 * a) - (40 * i) + (750 * i) + (975 * a) = 420 + 12000
(1725 * a) + (710 * i) = 12420
Now, we can solve for i:
i = (12420 - 1725 * a) / 710
Substituting this expression for i into the first equation, we get:
(75 * a) - (4 * ((12420 - 1725 * a) / 710)) = 42
Solving for a, we get:
a = 2
Substituting a = 2 into the expression for i, we get:
i = (12420 - 1725 * 2) / 710
i = 16
### Answer: a = 2, i = 16

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

Qwen2-Math 7B:

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

First, we can multiply the first equation by 27 and the second equation by 37 to make the coefficients of p equal:

1009 * p + 2028 * c = 4941
999 * c - 666 * p = 481

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

1009 * p + 2028 * c + 999 * c - 666 * p = 4941 + 481
1375 * c = 5422

Now, we can solve for c:

c = 5422 / 1375
c = <<5422/1375=3.94>>3.94

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

37 * p + 74 * 3.94 = 183
37 * p + 290.76 = 183
37 * p = 183 - 290.76
37 * p = -107.76

Now, we can solve for p:

p = -107.76 / 37
p = <<-107.76/37=-2.91>>-2.91

Therefore, the solution to the system of equations is p = -2.91 and c = 3.94.
### Answer: p = -2.91, c = 3.94

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method.
First, we can multiply the first equation by 16 and the second equation by 30 to make the coefficients of p equal:
(768 * k) - (480 * p) = 592
(480 * p) + (990 * k) = 3150
Now, we can add the two equations to eliminate p:
(768 * k) + (990 * k) = 3742
(1758 * k) = 3742
k = 3742 / 1758
k = <<3742/1758=2.13>>2.13
Now, we can substitute the value of k into one of the original equations to find p:
(48 * 2.13) - (30 * p) = 37
102.24 - (30 * p) = 37
-30 * p = 37 - 102.24
-30 * p = -65.24
p = -65.24 / -30
p = <<65.24/30=2.17>>2.17
### Answer: k = 2.13, p = 2.17

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 53 and the second equation by 69 to make the coefficients of v the same:

1. 3975v - 3657f = 742
2. 3174f + 3657v = 7590

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

3174f + 3657v - (3975v - 3657f) = 7590 - 742
3174f + 3657v - 3975v + 3657f = 6848
6831f = 6848
f = 6848/6831
f = <<6848/6831=0.999854>>0.999854

Now, we can substitute the value of f into one of the original equations to find the value of v:

75v - 69(0.999854) = 14
75v - 68.9879 = 14
75v = 82.9879
v = 82.9879/75
v = <<82.9879/75=1.106505>>1.106505

Therefore, the values for v and f that satisfy these simultaneous equations are v = <<82.9879/75=1.106505>>1.106505 and f = <<6848/6831=0.999854>>0.999854.
### Answer: v = 1.106505, f = 0.999854

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.

Qwen2-Math 7B:

 Reasoning: 
First, we can solve the first equation for o: 
o = (131 - 13 * g) / 7.
Substituting this into the second equation, we get: 
89 * g - 70 * ((131 - 13 * g) / 7) = 37.
Simplifying, we get: 
89 * g - 10 * (131 - 13 * g) = 37.
Expanding and simplifying, we get: 
89 * g - 1310 + 130 * g = 37.
Combining like terms, we get: 
219 * g = 1347.
Dividing both sides by 219, we get: 
g = 1347 / 219 = <<1347/219=6>>6.
Substituting this back into the equation for o, we get: 
o = (131 - 13 * 6) / 7 = <<(131-13*6)/7=5>>5.
### Answer: o = 5, g = 6

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the second equation by 60 to make the coefficients of k the same:
1980 * k - 660 * d = 2760
Now, we can subtract the first equation from this new equation to eliminate k:
1980 * k - 660 * d - (88 * d - 60 * k) = 2760 - 38
1920 * k - 748 * d = 2722
Now, we can solve for d:
d = (2722 - 1920 * k) / 748
Substituting this expression for d into the first equation, we can solve for k:
88 * ((2722 - 1920 * k) / 748) - 60 * k = 38
Solving this equation, we find that k = <<k=1>>1.
Substituting this value of k back into the expression for d, we find that d = <<d=2>>2.
### Answer: d = 2, k = 1

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination method.
Let's use the elimination method.
First, we can multiply the second equation by 12 to make the coefficients of z the same:
24 * z + 72 * y = 139,
24 * z + 984 * y = 1152.
Now, we can subtract the first equation from the second equation to eliminate z:
912 * y = 1013.
Dividing both sides by 912, we get:
y = <<1013/912=1.1111111111111112>>1.1111111111111112.
Substituting the value of y into the first equation, we get:
24 * z + 72 * 1.1111111111111112 = 139.
Solving for z, we get:
z = <<(139 - 72 * 1.1111111111111112) / 24=4.999999999999999>>4.999999999999999.
### Answer: y = 1.1111111111111112, z = 4.999999999999999

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 30 and the second equation by 29 to eliminate the variable o:
(2610 * o) - (870 * v) = 30
(232 * v) + (870 * o) = 2639
Now, we can add the two equations to eliminate the variable o:
(2610 * o) - (870 * v) + (232 * v) + (870 * o) = 30 + 2639
(3480 * o) - (638 * v) = 2669
Now, we can solve for the variable v:
v = (3480 * o - 2669) / 638
Next, we can substitute the value of v back into one of the original equations to solve for the variable o:
(87 * o) - (29 * ((3480 * o - 2669) / 638)) = 1
Now, we can solve for the variable o:
o = <<(87 * o) - (29 * ((3480 * o - 2669) / 638)) = 1>>1
Finally, we can substitute the value of o back into the equation for v to find the value of v:
v = (3480 * 1 - 2669) / 638
v = <<(3480 * 1 - 2669) / 638>>1
### Answer: v = 1, o = 1

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 11 and the second equation by 46 to make the coefficients of p the same:
(23 * h) - (46 * p) = 58 becomes (253 * h) - (506 * p) = 638
(11 * p) + (23 * h) = 124 becomes (506 * p) + (1058 * h) = 5616
Now, we can add the two equations to eliminate p:
(253 * h) - (506 * p) + (506 * p) + (1058 * h) = 638 + 5616
(1311 * h) = 6254
h = 6254 / 1311
h = <<6254/1311=4.77>>4.77
Now, we can substitute the value of h into one of the original equations to find p:
(23 * h) - (46 * p) = 58
(23 * 4.77) - (46 * p) = 58
110.71 - (46 * p) = 58
- (46 * p) = 58 - 110.71
- (46 * p) = -52.71
p = -52.71 / -46
p = <<-52.71/-46=1.15>>1.15
### Answer: h = 4.77, p = 1.15

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.

Qwen2-Math 7B:

 Reasoning: From the first equation, we can express f in terms of d: f = (120 - 19d)/6.
Substituting this expression into the second equation, we get: 90d - 42((120 - 19d)/6) = 69.
Solving this equation for d, we find that d = <<d value>>.
Substituting this value of d back into the expression for f, we find that f = <<f value>>.
### Answer: d = <<d value>>, f = <<f value>>

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'?

Qwen2-Math 7B:

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

First, we can multiply the first equation by 52 and the second equation by 55 to make the coefficients of 'r' in both equations equal:

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

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

5814 * m = 9024 

Dividing both sides by 5814, we get:

m = <<9024/5814=1.552>>1.552 

Substituting the value of 'm' in the first equation, we get:

42 * 1.552 + 55 * r = 127 

Solving for 'r', we get:

r = <<(127-42*1.552)/55=1.212>>1.212 

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

r = <<1.212>>1.212 
m = <<1.552>>1.552 
### Answer: r = 1.212, m = 1.552

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of linear equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 71 and the second equation by 64 to make the coefficients of n the same:
2191n + 4544w = 8400
3648w + 4544n = 11072
Next, we can subtract the second equation from the first equation to eliminate n:
2191n - 4544n = 8400 - 11072
-2353n = -2672
n = -2672/-2353 = <<-2672/-2353=1.134>>1.134
Now, we can substitute the value of n into one of the original equations to solve for w:
31(1.134) + 64w = 120
35.154 + 64w = 120
64w = 120 - 35.154
64w = 84.846
w = 84.846/64 = <<84.846/64=1.326>>1.326
Therefore, the values of n and w that satisfy the system of linear equations are n = 1.134 and w = 1.326.
### Answer: n = 1.134, w = 1.326

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.

Qwen2-Math 7B:

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

First, we can multiply equation 1 by 77 and equation 2 by 72 to make the coefficients of a equal:

1) 5424 * a + 1982 * u = 8464

2) 5424 * u - 5544 * a = 2232

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

5424 * a + 1982 * u + 5424 * u - 5544 * a = 8464 + 2232

This simplifies to:

-120 * a + 7406 * u = 10696

Now, we can solve for u:

u = 10696 / 7406 = <<10696/7406=1.44>>1.44

Substituting u = 1.44 into equation 1, we can solve for a:

72 * a + 26 * 1.44 = 112

72 * a + 37.44 = 112

72 * a = 112 - 37.44

72 * a = 74.56

a = 74.56 / 72 = <<74.56/72=1.03>>1.03

### Answer: a = 1.03, u = 1.44

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 3 and the second equation by 2 to make the coefficients of b the same:
162n + 54b = 429
174n - 186b = 96
Now, we can add the two equations to eliminate b:
336n = 525
n = 525/336 = <<525/336=1.5625>>
Now, we can substitute the value of n into the first equation to find the value of b:
54(1.5625) + 18b = 143
85.5 + 18b = 143
18b = 143 - 85.5 = <<143-85.5=57.5>>
b = 57.5/18 = <<57.5/18=3.1944>>
### Answer: b = 3.1944, n = 1.5625

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)?

Qwen2-Math 7B:

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

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

4664 * e + 616 * p = 8804
483 * e - 616 * p = 42

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

4664 * e + 483 * e = 8804 + 42
5147 * e = 8846

Now, we can solve for e:

e = 8846 / 5147
e = <<8846/5147=1.72>>1.72

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

53 * 1.72 + 7 * p = 103
91.84 + 7 * p = 103
7 * p = 103 - 91.84
7 * p = 11.16

Now, we can solve for p:

p = 11.16 / 7
p = <<11.16/7=1.59>>1.59

### Answer: e = 1.72, p = 1.59

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.

Qwen2-Math 7B:

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

First, we can multiply the first equation by 24 and the second equation by 7 to make the coefficients of p the same:

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

This gives us:

(432 * p) - (168 * s) = 504
(357 * s) - (168 * p) = 98

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

(432 * p) - (168 * s) + (357 * s) - (168 * p) = 504 + 98

This simplifies to:

(264 * p) + (189 * s) = 602

Now, we can solve for s:

s = (602 - (264 * p)) / 189

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

(18 * p) - (7 * ((602 - (264 * p)) / 189)) = 21

Solving this equation for p, we get:

p = <<(21 + (7 * (602 / 189))) / (18 - (7 * (264 / 189)))>>1.5

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

s = (602 - (264 * 1.5)) / 189

s = <<(602 - (264 * 1.5)) / 189>>1.5

Therefore, the values of p and s that satisfy both equations are:

p = 1.5
s = 1.5

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

Correct? No

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 11 and the second equation by 59 to make the coefficients of c the same:
59*11c - 34*11w = 84*11
59*59c + 42*59w = 98*59
Now, we can add the two equations to eliminate c:
(59*11c - 34*11w) + (59*59c + 42*59w) = 84*11 + 98*59
59*11c + 59*59c = 84*11 + 98*59
59*(11c + 59c) = 84*11 + 98*59
59*70c = 84*11 + 98*59
Now, we can solve for c:
c = (84*11 + 98*59) / (59*70)
c = (924 + 5782) / 4130
c = 6706 / 4130
c = <<6706/4130=1.624>>1.624
Now, we can substitute the value of c back into one of the original equations to solve for w:
59c - 34w = 84
59*1.624 - 34w = 84
96.896 - 34w = 84
-34w = 84 - 96.896
-34w = -12.896
w = -12.896 / -34
w = <<-12.896/-34=0.379>>0.379
### Answer: c = 1.624, w = 0.379

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.

Qwen2-Math 7B:

 Reasoning: 
First, we can solve the first equation for f: f = (101 - 42 * z) / 45.
Next, we can substitute this expression for f into the second equation: 60 * z - 42 * ((101 - 42 * z) / 45) = 13.
Simplifying this equation, we get: 60 * z - (42 * 101 - 42 * 42 * z) / 45 = 13.
Multiplying both sides by 45, we get: 2700 * z - 42 * 101 + 42 * 42 * z = 585.
Combining like terms, we get: 1146 * z = 1015.
Dividing both sides by 1146, we get: z = 1015 / 1146.
Substituting this value of z back into the expression for f, we get: f = (101 - 42 * (1015 / 1146)) / 45.
Simplifying this expression, we get: f = (101 - 42 * 1015 / 1146) / 45.
Therefore, the solution to the system of equations is f = <<(101 - 42 * 1015 / 1146) / 45>> and z = <<1015 / 1146>>.
### Answer: f = <<(101 - 42 * 1015 / 1146) / 45>>, z = <<1015 / 1146>>

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.

Qwen2-Math 7B:

 Reasoning: 
First, we can solve the system of equations using the method of substitution or elimination. Let's use elimination.
Multiply the first equation by 15 and the second equation by 26 to eliminate p:
390 * p - 315 * u = 90 
390 * p + 1508 * u = 2158
Subtract the first equation from the second equation:
1823 * u = 2068
u = <<1823/2068=0.881>>0.881
Substitute u = 0.881 into the first equation:
26 * p - 21 * 0.881 = 6
26 * p = 6 + 18.491
p = <<(6+18.491)/26=0.934>>0.934
### Answer: p = 0.934, u = 0.881

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 8 and the second equation by 38 to make the coefficients of s the same:
1) 736 * n - 304 * s = 496
2) 2242 * n + 304 * s = 2850
Now, we can add the two equations to eliminate s:
736 * n + 2242 * n = 496 + 2850
2978 * n = 3346
n = 3346 / 2978
n = <<3346/2978=1.12>>1.12
Now, we can substitute the value of n into one of the original equations to solve for s:
92 * 1.12 - 38 * s = 62
102.24 - 38 * s = 62
-38 * s = 62 - 102.24
-38 * s = -40.24
s = -40.24 / -38
s = <<-40.24/-38=1.06>>1.06
### Answer: n = 1.12, s = 1.06

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 58 and the second equation by 35 to make the coefficients of e the same:
58 * (87 * z - 35 * e) = 58 * 63
35 * (81 * z + 58 * e) = 35 * 154
This gives us:
4986 * z - 2030 * e = 3654
2835 * z + 2030 * e = 5390
Now, we can add these two equations to eliminate e:
4986 * z + 2835 * z = 3654 + 5390
7821 * z = 9044
z = <<7821/9044=0.864>>0.864
Now, we can substitute the value of z back into one of the original equations to find e:
87 * 0.864 - 35 * e = 63
75.288 - 35 * e = 63
-35 * e = 63 - 75.288
-35 * e = -12.288
e = <<-12.288/-35=0.351>>0.351
### Answer: e = 0.351, z = 0.864

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.

Qwen2-Math 7B:

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

First, we can multiply the first equation by 36 and the second equation by 44 to make the coefficients of h the same:

(396 * t) + (1584 * h) = 3960
(4232 * t) - (1584 * h) = 792.

Next, we can add the two equations to eliminate h:

(4628 * t) = 4752.

Now, we can solve for t:

t = 4752 / 4628 = <<4752/4628=1.026>>1.026.

Substituting the value of t back into the first equation, we can solve for h:

(11 * 1.026) + (44 * h) = 110,
44 * h = 110 - 11.286,
h = (110 - 11.286) / 44 = <<(110-11.286)/44=2.21>>2.21.

Therefore, the values of h and t are h = <<2.21>>2.21 and t = <<1.026>>1.026.

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of linear equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 18 and the second equation by 50 to eliminate the variable o:
(18 * (69 * b) - (18 * 50 * o)) = 18 * 55
(50 * (41 * o) + (50 * 18 * b)) = 50 * 85
Simplifying the equations, we get:
(1242 * b - 900 * o) = 990
(2050 * o + 900 * b) = 4250
Now, we can add the two equations to eliminate the variable o:
(1242 * b - 900 * o) + (2050 * o + 900 * b) = 990 + 4250
Simplifying the equation, we get:
(1242 * b + 900 * b) = 5240
(2142 * b) = 5240
Dividing both sides by 2142, we get:
b = <<5240/2142=2.44>>2.44
Now, we can substitute the value of b into one of the original equations to find the value of o:
(69 * 2.44) - (50 * o) = 55
168.36 - (50 * o) = 55
Subtracting 168.36 from both sides, we get:
-50 * o = -113.36
Dividing both sides by -50, we get:
o = <<-113.36/-50=2.27>>2.27
### Answer: b = 2.44, o = 2.27

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

Correct? No

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the second equation by 10 to make the coefficients of q the same: 60 * q + 50 * p = 1770.
Now, we can subtract the first equation from this new equation to eliminate q: 60 * q + 50 * p - (67 * q - 80 * p) = 1770 - 65.
This simplifies to -7 * q + 130 * p = 1705.
Now, we can solve for p: p = (1705 + 7 * q) / 130.
Substituting this expression for p into the second equation, we get: 6 * q + 5 * ((1705 + 7 * q) / 130) = 177.
Solving this equation for q, we get q = <<67q-80p=65; 6q+5p=177; q=(1705+7q)/130; 6q+5((1705+7q)/130)=177; q=13; p=11>>13.
Substituting this value of q into the expression for p, we get p = <<67q-80p=65; 6q+5p=177; q=(1705+7q)/130; 6q+5((1705+7q)/130)=177; q=13; p=11>>11.
### Answer: p = <<67q-80p=65; 6q+5p=177; q=(1705+7q)/130; 6q+5((1705+7q)/130)=177; q=13; p=11>>11, q = <<67q-80p=65; 6q+5p=177; q=(1705+7q)/130; 6q+5((1705+7q)/130)=177; q=13; p=11>>13

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 41 and the second equation by 48 to make the coefficients of f equal:
410 * k + 1968 * f = 6601
1584 * k - 1968 * f = 1488
Now, we can add the two equations to eliminate f:
410 * k + 1584 * k = 6601 + 1488
1994 * k = 8089
k = 8089 / 1994
k = <<8089/1994=4.05>>4.05
Now, we can substitute the value of k into one of the original equations to find f:
10 * 4.05 + 48 * f = 161
40.5 + 48 * f = 161
48 * f = 161 - 40.5
48 * f = 120.5
f = 120.5 / 48
f = <<120.5/48=2.51>>2.51
### Answer: k = 4.05, f = 2.51

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

Qwen2-Math 7B:

 Reasoning: 
From the first equation, we can express n in terms of l: n = 58 * l - 31.
Substituting this expression for n into the second equation, we get: 103 = (58 * l - 31) + 73 * l.
Simplifying this equation, we get: 103 = 131 * l - 31.
Adding 31 to both sides, we get: 134 = 131 * l.
Dividing both sides by 131, we get: l = 134 / 131 = <<134/131=1.0225563909774431>>1.0225563909774431.
Substituting this value of l back into the expression for n, we get: n = 58 * 1.0225563909774431 - 31 = <<58*1.0225563909774431-31=27.288000000000002>>27.288000000000002.
### Answer: l = <<134/131=1.0225563909774431>>1.0225563909774431, n = <<58*1.0225563909774431-31=27.288000000000002>>27.288000000000002

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

Qwen2-Math 7B:

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

First, we can multiply the first equation by 25 and the second equation by 29 to make the coefficients of y the same:

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

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

1773j = 2389

Now, we can solve for j:

j = 2389 / 1773 = <<2389/1773=1.346>>1.346

Finally, we can substitute the value of j back into one of the original equations to solve for y:

29y - 28(1.346) = 39
29y - 37.688 = 39
29y = 76.688
y = 76.688 / 29 = <<76.688/29=2.644>>2.644

### Answer: y = 2.644, j = 1.346

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.

Qwen2-Math 7B:

 Reasoning: 
First, we can multiply the first equation by 17 and the second equation by 85 to eliminate a:
1581u - 1445a = 1258
8160u + 1445a = 15810
Adding these two equations, we get:
9741u = 17068
Dividing both sides by 9741, we get:
u = <<17068/9741=1.75>>1.75
Substituting u = 1.75 into the first equation, we get:
93(1.75) - 85a = 74
162.75 - 85a = 74
Subtracting 162.75 from both sides, we get:
-85a = -88.75
Dividing both sides by -85, we get:
a = <<-88.75/-85=1.0447>>1.0447
### Answer: u = 1.75, a = 1.0447

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

Qwen2-Math 7B:

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

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

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

This gives us:

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

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

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

Now, we can solve for u:

u = 11691 / 7416
u = <<11691/7416=1.57>>1.57

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

97 * 1.57 - 61 * g = 15

Now, we can solve for g:

151.29 - 61 * g = 15
-61 * g = 15 - 151.29
-61 * g = -136.29

Now, we can solve for g:

g = -136.29 / -61
g = <<-136.29/-61=2.23>>2.23

### Answer: u = 1.57, g = 2.23

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.

Qwen2-Math 7B:

 Reasoning: Subtracting the first equation from the second equation, we get (85 * r) - (17 * r) = 187 - 103, which simplifies to 68 * r = 84. Dividing both sides by 68, we get r = <<84/68=1.2352941176470588>>1.2352941176470588. Substituting this value of r into the first equation, we get (17 * 1.2352941176470588) + (67 * b) = 103, which simplifies to 21.000000000000004 + (67 * b) = 103. Subtracting 21.000000000000004 from both sides, we get 67 * b = 81.99999999999999. Dividing both sides by 67, we get b = <<81.99999999999999/67=1.2298507462686567>>1.2298507462686567.
### Answer: r = 1.2352941176470588, b = 1.2298507462686567

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.

Qwen2-Math 7B:

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

First, we can multiply the first equation by 30 and the second equation by 54 to make the coefficients of n the same:

1. (2550 * n) - (1620 * t) = 1230
2. (2052 * t) + (1530 * n) = 6804

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

(2550 * n) - (1620 * t) + (2052 * t) + (1530 * n) = 1230 + 6804

This simplifies to:

(4080 * n) - (568 * t) = 8034

Now, we can solve for t:

t = (4080 * n - 8034) / 568

Substituting this expression for t back into one of the original equations, we can solve for n:

(85 * n) - (54 * ((4080 * n - 8034) / 568)) = 41

Solving this equation, we find that n = <<41>>41.

Substituting n = 41 back into the expression for t, we find that t = <<568>>568.

### Answer: t = 568, n = 41

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.

Qwen2-Math 7B:

 Reasoning: From the first equation, we can express u in terms of q: u = (5 + 69q) / 75.
Substituting this expression into the second equation, we get: 48((5 + 69q) / 75) + 25q = 140.
Solving this equation for q, we find that q = <<48((5 + 69q) / 75) + 25q = 140|solve for q>>.
Substituting this value of q back into the expression for u, we find that u = <<u = (5 + 69q) / 75>>.
### Answer: u = <<u = (5 + 69q) / 75>>, q = <<48((5 + 69q) / 75) + 25q = 140|solve for q>>

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination method.
Let's use the elimination method.
First, we can multiply the first equation by 49 and the second equation by 17 to make the coefficients of v equal.
49 * ((20 * v) + (17 * x)) = 49 * 149
17 * ((24 * x) - (49 * v)) = 17 * 22
This gives us:
980 * v + 833 * x = 7201
408 * x - 833 * v = 374
Now, we can add these two equations to eliminate v:
980 * v + 833 * x + 408 * x - 833 * v = 7201 + 374
1241 * x = 7575
x = <<1241/7575=0.164>>0.164
Now, we can substitute the value of x back into one of the original equations to find v.
Let's use the first equation:
(20 * v) + (17 * 0.164) = 149
20 * v = 149 - 2.828
20 * v = 146.172
v = <<146.172/20=7.309>>7.309
### Answer: v = 7.309, x = 0.164

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method.
First, we can multiply the first equation by 91 and the second equation by 41 to make the coefficients of g the same:
3549 * t + 3711 * g = 13239
3854 * t - 3711 * g = 1722
Adding these two equations, we get:
7403 * t = 14961
Dividing both sides by 7403, we get:
t = <<14961/7403=2>>2
Substituting this value of t into the first equation, we get:
39 * 2 + 41 * g = 147
78 + 41 * g = 147
Subtracting 78 from both sides, we get:
41 * g = 69
Dividing both sides by 41, we get:
g = <<69/41=1.68>>1.68
### Answer: t = 2, g = 1.68

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

Correct? No

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 55 and the second equation by 6 to make the coefficients of c the same:
330c + 3025o = 6160
330c - 288o = 216
Now, we can subtract the second equation from the first equation to eliminate c:
3025o - (-288o) = 6160 - 216
3313o = 5944
o = <<3313/5944=0.557>>0.557
Now, we can substitute the value of o back into one of the original equations to find the value of c:
6c + 55(0.557) = 112
6c + 30.635 = 112
6c = 81.365
c = <<81.365/6=13.561>>13.561
Therefore, the values of c and o that satisfy the system of equations are c = 13.561 and o = 0.557.
### Answer: c = 13.561, o = 0.557

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use elimination.
First, we can multiply the first equation by 94 and the second equation by 68 to make the coefficients of u the same:
7672w + 6368u = 15980,
4828w - 6368u = 544.
Adding these two equations, we get:
12500w = 16524.
Dividing both sides by 12500, we get:
w = <<16524/12500=1.32192>>1.32192.
Substituting this value of w into the first equation, we get:
8(1.32192) + 68u = 170.
Solving for u, we get:
u = <<(170-8(1.32192))/68=2.4142857142857144>>2.4142857142857144.
### Answer: u = 2.4142857142857144, w = 1.32192

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 38 and the second equation by 68 to make the coefficients of r the same:

2584*r + 296*f = 3456
6596*f + 2584*r = 12416

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

6596*f - 296*f = 12416 - 3456
6300*f = 8960
f = 8960/6300 = <<8960/6300=1.4285714285714286>>1.4285714285714286

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

68*r + 8*1.4285714285714286 = 92
68*r + 11.428571428571429 = 92
68*r = 92 - 11.428571428571429
68*r = 80.57142857142857
r = 80.57142857142857/68 = <<80.57142857142857/68=1.1852941176470588>>1.1852941176470588

### Answer: r = 1.1852941176470588, f = 1.4285714285714286

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).

Qwen2-Math 7B:

 Reasoning: We have two equations:

67d - 37r = 50
39r - 21d = 16

To solve for d and r, we can use the method of substitution or elimination. Let's use elimination.

First, we can multiply the first equation by 21 and the second equation by 67 to make the coefficients of d the same:

1407d - 777r = 1050
2553r - 1407d = 1072

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

1407d - 777r + 2553r - 1407d = 1050 + 1072
1776r = 2122

Now, we can solve for r:

r = 2122 / 1776
r = <<2122/1776=1.2}}1.2

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

67d - 37(1.2) = 50
67d - 44.4 = 50
67d = 94.4
d = 94.4 / 67
d = <<94.4/67=1.4}}1.4

Therefore, the cost of each apple (d) is $1.4, and the cost of each ragdoll (r) is $1.2.

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.

Qwen2-Math 7B:

 Reasoning: 
First, we can simplify the first equation to 163 = 50x + a.
Then, we can simplify the second equation to 24 = 98x - 84a.
Next, we can solve for a in the first equation: a = 163 - 50x.
Substituting this expression for a into the second equation, we get 24 = 98x - 84(163 - 50x).
Simplifying this equation, we get 24 = 98x - 13752 + 4200x.
Combining like terms, we get 4298x = 13776.
Dividing both sides by 4298, we get x = <<4298/13776=0.3125>>0.3125.
Substituting this value of x back into the expression for a, we get a = 163 - 50(0.3125) = <<163-50*0.3125=140>>140.
### Answer: x = 0.3125, a = 140

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 44 and the second equation by 67 to make the coefficients of p equal:
2948 * p + 792 * b = 4840
5494 * b - 2948 * p = 3896
Now, we can add the two equations to eliminate p:
792 * b + 5494 * b = 4840 + 3896
6286 * b = 8736
b = <<6286/8736=0.716>>0.716
Now, we can substitute the value of b into the first equation to find p:
67 * p + 18 * 0.716 = 110
67 * p = 110 - 12.888
p = <<(110-12.888)/67=1.32>>1.32
### Answer: p = 1.32, b = 0.716

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.

Qwen2-Math 7B:

 Reasoning: 
63c - 36e = 27
8c + 32e = 69

Solving the system of equations, we get:
c = <<63c - 36e = 27, 8c + 32e = 69|solve for c and e>>1
e = <<63c - 36e = 27, 8c + 32e = 69|solve for c and e>>2

Therefore, the values of c and e are:
c = <<63c - 36e = 27, 8c + 32e = 69|solve for c and e>>1
e = <<63c - 36e = 27, 8c + 32e = 69|solve for c and e>>2

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

Qwen2-Math 7B:

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

First, we can multiply the first equation by 51 and the second equation by 29 to make the coefficients of p the same:

1356 * x + 1479 * p = 5457 

1769 * x - 1479 * p = 116

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

3125 * x = 5573

Now, we can solve for x:

x = <<3125/5573=0.560>>0.560

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

26 * 0.560 + 29 * p = 107

14.56 + 29 * p = 107

29 * p = 92.44

p = <<92.44/29=3.187>>3.187

### Answer: x = 0.560, p = 3.187

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From the first equation, we can express l in terms of g: l = (68 - 17g) / 29.
Substituting this expression for l into the second equation, we get: (31g - 10((68 - 17g) / 29)) = 17.
Solving for g, we get: g = <<31g - 10((68 - 17g) / 29) = 17>>1.
Substituting g = 1 into the expression for l, we get: l = (68 - 17(1)) / 29 = <<(68 - 17(1)) / 29>>2.
### Answer: g = 1, l = 2

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method.
First, we can multiply the second equation by 33/24 to make the coefficients of a the same in both equations:

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

Simplifying the second equation, we get:

33*a - 54*c = 20 
33*a - 33*c = 33*29/24

Subtracting the second equation from the first, we get:

-21*c = 20 - 33*29/24

Solving for c, we get:

c = (20 - 33*29/24)/-21 = <<(20 - 33*29/24)/-21=1>>1

Substituting c = 1 into the first equation, we get:

33*a - 54*1 = 20

Solving for a, we get:

a = (20 + 54)/33 = <<(20 + 54)/33=2>>2

Therefore, the values for a and c are a = <<2>>2 and c = <<1>>1.
### Answer: a = 2, c = 1

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 84 and the second equation by 71 to make the coefficients of d the same:
5884d + 756j = 10968
3053j - 5964d = 6491
Now, we can add the two equations to eliminate d:
5884d + 756j + 3053j - 5964d = 10968 + 6491
3809j = 17459
j = <<3809/17459=2.18>>2.18
Now, we can substitute the value of j back into one of the original equations to find d:
71d + 9(2.18) = 132
71d + 19.62 = 132
71d = 112.38
d = <<112.38/71=1.58>>1.58
### Answer: d = 1.58, j = 2.18

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.

Qwen2-Math 7B:

 Reasoning: 
(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143
Solving this system of equations, we get:
o = <<81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=163;87*n+23*o=143;81*o+26*n=

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Here, we will use the method of elimination.
First, we can multiply the first equation by 61 and the second equation by 46 to eliminate s:

2886 * s - 3721 * w = 122 
2886 * s + 3062 * w = 8188.
Subtracting the first equation from the second equation, we get:

6783 * w = 8066.
Dividing both sides by 6783, we get:

w = <<8066/6783=1.19>>1.19.
Substituting this value of w into the first equation, we get:

46 * s - 61 * 1.19 = 2.
Simplifying, we get:

46 * s = 85.79.
Dividing both sides by 46, we get:

s = <<85.79/46=1.86>>1.86.
### Answer: w = 1.19, s = 1.86

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 8 and the second equation by 51 to make the coefficients of k the same:
408*k - 64*i = 688
1989*i + 408*k = 9753
Now, we can subtract the first equation from the second equation to eliminate k:
1989*i - 64*i = 9753 - 688
1925*i = 9065
i = <<1925/1925=9065/1925=4.71>>4.71
Now, we can substitute the value of i into the first equation to find the value of k:
51*k - 8*4.71 = 86
51*k = 86 + 37.68
51*k = 123.68
k = <<123.68/51=2.42>>2.42
### Answer: i = 4.71, k = 2.42

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the second equation by 17 to make the coefficients of l the same:
1591m + 17l = 2142
Now, we can subtract the first equation from this new equation to eliminate l:
1591m + 17l - (26m + 17l) = 2142 - 146
1565m = 1996
m = <<1565/1565=1>>1
Now, we can substitute this value of m back into one of the original equations to solve for l:
26(1) + 17l = 146
17l = 120
l = <<120/17>><<120/17=7.05882352941>>7.05882352941
### Answer: l = 7.05882352941, m = 1

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

Qwen2-Math 7B:

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

First, we can multiply the first equation by 29 and the second equation by 8 to make the coefficients of 'f' the same:

1) (232 * f) + (1131 * h) = 1914

2) (232 * f) + (368 * h) = 952

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

(1131 * h) - (368 * h) = 1914 - 952

763 * h = 962

h = 962 / 763

h = <<962/763=1.26>>1.26

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

(8 * f) + (39 * 1.26) = 66

(8 * f) + 49.14 = 66

(8 * f) = 66 - 49.14

(8 * f) = 16.86

f = 16.86 / 8

f = <<16.86/8=2.1075>>2.1075

### Answer: h = 1.26, f = 2.1075

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 69 and the second equation by 23 to make the coefficients of b equal:
1518 * b + 1517 * k = 7443
1426 * k - 1587 * b = 322
Now, we can add the two equations to eliminate b:
1517 * k = 7765
k = <<1517/7765=0.1949>>0.1949
Substituting k = 0.1949 into the first equation, we get:
22 * b + 23 * 0.1949 = 109
22 * b = 109 - 4.4827
b = <<(109-4.4827)/22=4.82>>4.82
### Answer: k = 0.1949, b = 4.82

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.

Qwen2-Math 7B:

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

First, we can multiply the second equation by 55 to make the coefficients of s the same:

1. 84m - 55s = 1
2. 3465m - 110s = 5390

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

3465m - 110s - (84m - 55s) = 5390 - 1
3381m = 5389

Now, we can solve for m:

m = 5389 / 3381
m = <<5389/3381=1.6000>>1.6000

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

84(1.6000) - 55s = 1
134.4 - 55s = 1
-55s = 1 - 134.4
-55s = -133.4

Now, we can solve for s:

s = -133.4 / -55
s = <<-133.4/-55=2.4254>>2.4254

### Answer: m = 1.6000, s = 2.4254

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.

Qwen2-Math 7B:

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

From equation 1, we can express b in terms of k:
b = (105 - 5k) / 6

Substitute this expression for b into equation 2:
95k - 51((105 - 5k) / 6) = 67

Solve for k:
k = <<95k - 51((105 - 5k) / 6) = 67, solve for k>>1

Substitute the value of k back into the expression for b:
b = (105 - 5(1)) / 6
b = <<(105 - 5(1)) / 6>>10

### Answer: b = 10, k = 1

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 40 and the second equation by 33 to make the coefficients of d the same:
1320d + 2480u = 4560
1056u + 1320d = 2739
Subtracting the second equation from the first, we get:
1424u = 1821
u = <<1821/1424=1.28>>1.28
Substituting u = 1.28 into the first equation, we get:
33d + 62(1.28) = 114
33d + 79.36 = 114
33d = 34.64
d = <<34.64/33=1.05>>1.05
### Answer: d = 1.05, u = 1.28

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

Qwen2-Math 7B:

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

First, we can multiply the first equation by 4 to make the coefficients of c the same:

20 * c + 112 * p = 408

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

(20 * c + 112 * p) - (20 * c - 67 * p) = 408 - 13

This simplifies to:

179 * p = 395

Now, we can solve for p:

p = 395 / 179

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

5 * c + 28 * (395 / 179) = 102

This simplifies to:

5 * c + 56 = 102

Now, we can solve for c:

5 * c = 102 - 56

5 * c = 46

c = 46 / 5

So, the values of c and p are:

c = <<46/5=9.2>>9.2
p = <<395/179=2.2>>2.2
### Answer: c = 9.2, p = 2.2

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use elimination. Multiply the first equation by 76 and the second equation by 58 to eliminate r:
4328 * r + 912 * q = 11088
-4328 * r + 5584 * q = 4408
Adding these two equations, we get:
6496 * q = 15496
q = <<15496/6496=2.388>>2.388
Substituting q back into the first equation:
58 * r + 12 * 2.388 = 147
58 * r = 147 - 28.656
r = <<(147-28.656)/58=1.96>>1.96
### Answer: r = 1.96, q = 2.388

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method.
First, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of k the same:
94 * v - 6 * k = 20
219 * v + 6 * k = 384
Now, we can add the two equations to eliminate k:
313 * v = 404
v = <<313/404=0.774>>0.774
Now, we can substitute the value of v into one of the original equations to find k:
47 * 0.774 - 3 * k = 10
36.378 - 3 * k = 10
3 * k = 26.378
k = <<26.378/3=8.792666666666667>>8.792666666666667
### Answer: v = 0.774, k = 8.792666666666667

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?

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 27 and the second equation by 89 to make the coefficients of p the same:
27(89p - 41q) = 27(60)
89(27p + 91q) = 89(124)
This gives us:
2403p - 1107q = 1620
2403p + 8099q = 11036
Now, we can subtract the first equation from the second equation to eliminate p:
(2403p + 8099q) - (2403p - 1107q) = 11036 - 1620
This simplifies to:
9206q = 9416
Now, we can solve for q:
q = 9416 / 9206
q = <<9416/9206=1.022>>1.022
Now that we have the value of q, we can substitute it back into one of the original equations to solve for p. Let's use the first equation:
89p - 41(1.022) = 60
89p - 42.002 = 60
89p = 102.002
p = 102.002 / 89
p = <<102.002/89=1.146>>1.146
Therefore, the values of p and q are p = <<1.146>>1.146 and q = <<1.022>>1.022.
### Answer: p = 1.146, q = 1.022

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

Qwen2-Math 7B:

 Reasoning: 
First, we can simplify the first equation by dividing both sides by 8: 
11u - 12d = 1.5
Next, we can simplify the second equation by dividing both sides by 9: 
3u + 4d = 7.89
Now we have a system of two equations with two variables: 
11u - 12d = 1.5
3u + 4d = 7.89
We can solve this system of equations using the substitution or elimination method. 
Using the substitution method, we can solve the second equation for u: 
u = (7.89 - 4d) / 3
Substituting this expression for u into the first equation, we get: 
11((7.89 - 4d) / 3) - 12d = 1.5
Simplifying this equation, we get: 
26.37 - 44d - 36d = 4.5
Combining like terms, we get: 
-80d = -21.87
Dividing both sides by -80, we get: 
d = 0.273375
Substituting this value of d back into the expression for u, we get: 
u = (7.89 - 4(0.273375)) / 3
Simplifying this expression, we get: 
u = 2.23
Therefore, the values of u and d that make these equations true are: 
u = 2.23
d = 0.273375
### Answer: u = 2.23, d = 0.273375

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.

Qwen2-Math 7B:

 Reasoning: From the second equation, we can express n in terms of f: n = (70 + 2f) / 3.
Substituting this into the first equation, we get: 20 * ((70 + 2f) / 3) - 18 * f = 9.
Solving this equation for f, we find that f = <<20 * ((70 + 2f) / 3) - 18 * f = 9; f = 10>>10.
Substituting f = 10 into the equation n = (70 + 2f) / 3, we find that n = <<n = (70 + 2f) / 3; n = 30>>30.
### Answer: f = 10, n = 30

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use elimination.
First, we can multiply the first equation by 22 and the second equation by 7 to make the coefficients of j the same:
154 * l + 2134 * j = 2926
154 * j + 259 * l = 532
Subtracting the second equation from the first, we get:
1995 * j = 2394
j = <<1995/2394=0.8333333333333334>>0.8333333333333334
Substituting j back into the first equation, we get:
7 * l + 97 * 0.8333333333333334 = 133
7 * l = 133 - 81.66666666666667
l = <<(133 - 81.66666666666667)/7=7.285714285714286>>7.285714285714286
### Answer: j = 0.8333333333333334, l = 7.285714285714286

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method.
First, we can multiply the first equation by 8 and the second equation by 21 to make the coefficients of d the same:

168d - 368f = 424 
168d + 1764f = 2793
Next, we can subtract the first equation from the second equation to eliminate d:

2132f = 2369
Now, we can solve for f:

f = 2369/2132 = <<2369/2132=1.1099>>1.1099
Finally, we can substitute the value of f back into one of the original equations to solve for d:

21d - 46(1.1099) = 53
21d - 50.9554 = 53
21d = 103.9554
d = 103.9554/21 = <<103.9554/21=4.9502>>4.9502
### Answer: d = 4.9502, f = 1.1099

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 68 and the second equation by 11 to make the coefficients of w the same:
68(74u + 11w) = 68(116)
11(66u - 68w) = 11(21)
This gives us:
4952u + 748w = 7888
726u - 748w = 231
Now, we can add the two equations to eliminate w:
4952u + 748w + 726u - 748w = 7888 + 231
5678u = 8119
Now, we can solve for u:
u = 8119 / 5678
u = <<8119/5678=1.43>>1.43
Now, we can substitute the value of u back into one of the original equations to solve for w:
74(1.43) + 11w = 116
105.62 + 11w = 116
11w = 116 - 105.62
11w = 10.38
w = 10.38 / 11
w = <<10.38/11=0.94>>0.94
### Answer: u = 1.43, w = 0.94

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 47 and the second equation by 76 to make the coefficients of f equal:
47 * (76 * f - 42 * j) = 47 * 96
76 * (47 * j + 34 * f) = 76 * 136
This gives us:
3572 * f - 1974 * j = 4512
3572 * j + 2584 * f = 10256
Now, we can subtract the first equation from the second equation to eliminate f:
(3572 * j + 2584 * f) - (3572 * f - 1974 * j) = 10256 - 4512
This simplifies to:
5546 * j = 5744
Now, we can solve for j:
j = 5744 / 5546
j = <<5744/5546=1.034>>1.034
Now, we can substitute the value of j back into one of the original equations to solve for f:
76 * f - 42 * 1.034 = 96
76 * f = 96 + 42 * 1.034
76 * f = 96 + 43.428
76 * f = 139.428
f = 139.428 / 76
f = <<139.428/76=1.832>>1.832
### Answer: f = 1.832, j = 1.034

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 63 and the second equation by 68 to make the coefficients of u the same:
4176u + 2016e = 10878
4536e - 4743u = 68
Now, we can add the two equations to eliminate u:
2016e + 4536e = 10878 + 68
6552e = 10946
e = <<6552e=10946>>10946/6552 = <<10946/6552=1.67>>1.67
Now, we can substitute the value of e back into one of the original equations to find u:
68u + 32(1.67) = 174
68u + 53.44 = 174
68u = 120.56
u = <<68u=120.56>>120.56/68 = <<120.56/68=1.77>>1.77
### Answer: u = 1.77, e = 1.67

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of linear equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the first equation by 39 and the second equation by 4 to make the coefficients of n the same:
2223p + 156n = 5031
96p + 156n = 616
Now, we can subtract the second equation from the first equation to eliminate n:
2223p - 96p = 5031 - 616
2127p = 4415
p = <<2127/4415=0.4818>>0.4818
Now, we can substitute the value of p into one of the original equations to find the value of n:
57(0.4818) + 4n = 129
27.54 + 4n = 129
4n = 101.46
n = <<101.46/4=25.365>>25.365
Therefore, the values of p and n that satisfy the system of linear equations are p = 0.4818 and n = 25.365.
### Answer: p = 0.4818, n = 25.365

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method.
First, we can multiply the first equation by 14 and the second equation by 44 to make the coefficients of z the same:
924 * z - 616 * y = 448 
2640 * y + 616 * z = 5056.
Next, we can add the two equations to eliminate z:
924 * z + 2640 * y = 5504.
Now, we can solve for y:
2640 * y = 5504 - 924 * z
y = (5504 - 924 * z) / 2640.
Substituting this expression for y into the first equation, we get:
66 * z - 44 * ((5504 - 924 * z) / 2640) = 32.
Simplifying this equation, we get:
66 * z - (5504 - 924 * z) / 60 = 32.
Multiplying both sides by 60, we get:
3960 * z - 5504 + 924 * z = 1920.
Combining like terms, we get:
4884 * z = 7424.
Dividing both sides by 4884, we get:
z = 7424 / 4884 = <<7424/4884=1.52>>1.52.
Substituting this value of z back into the expression for y, we get:
y = (5504 - 924 * 1.52) / 2640 = <<(5504-924*1.52)/2640=1.6>>1.6.
### Answer: y = 1.6, z = 1.52

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.

Qwen2-Math 7B:

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

First, we can multiply the first equation by 11 and the second equation by 58 to make the coefficients of t the same:

11 * (83 * t - 58 * h) = 11 * 45
58 * (69 * h + 11 * t) = 58 * 124

This gives us:

913 * t - 638 * h = 495
3942 * h + 638 * t = 7192

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

913 * t - 638 * h + 3942 * h + 638 * t = 495 + 7192

This simplifies to:

4855 * h = 7687

Now, we can solve for h:

h = 7687 / 4855

Now that we have the value of h, we can substitute it back into one of the original equations to find t. Let's use the first equation:

83 * t - 58 * (7687 / 4855) = 45

Now, we can solve for t:

t = (45 + 58 * (7687 / 4855)) / 83

### Answer: t = <<(45 + 58 * (7687 / 4855)) / 83>>, h = <<7687 / 4855>>

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?

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From the first equation, we can express h in terms of o: h = (9 + 61 * o) / 79.
Substituting this expression for h into the second equation, we get: ((16 * ((9 + 61 * o) / 79)) - (12 * o)) = 9.
Solving this equation for o, we get: o = <<(16 * ((9 + 61 * o) / 79)) - (12 * o) = 9, solve for o>>.
Substituting the value of o back into the expression for h, we get: h = <<(9 + 61 * o) / 79>>.
### Answer: o = <<(16 * ((9 + 61 * o) / 79)) - (12 * o) = 9, solve for o>>, h = <<(9 + 61 * o) / 79>>

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the method of substitution or elimination. Let's use the method of elimination.
First, we can multiply the first equation by 90 and the second equation by 56 to make the coefficients of s equal:

360 * y + 5040 * s = 12510

3640 * y - 5040 * s = 896

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.

Qwen2-Math 7B:

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

First, we can multiply the first equation by 45 and the second equation by 4 to make the coefficients of z the same:

1890 * d - 180 * z = 3375
160 * d + 180 * z = 648

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

1890 * d + 160 * d = 3375 + 648
2050 * d = 4023

Now, we can solve for d:

d = 4023 / 2050
d = <<4023/2050=2.001>>2.001

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

42 * 2.001 - 4 * z = 75
84.042 - 4 * z = 75
-4 * z = 75 - 84.042
-4 * z = -9.042

Now, we can solve for z:

z = -9.042 / -4
z = <<-9.042/-4=2.2605>>2.2605

### Answer: d = 2.001, z = 2.2605

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination method.
Let's use the elimination method.
First, we can multiply the second equation by 4 to make the coefficients of 'o' the same:
(42 * a) + (6 * o) = 75
(168 * a) + (24 * o) = 300
Now, we can subtract the first equation from this new equation:
(168 * a) + (24 * o) - (42 * o) - (24 * a) = 300 - 142
(144 * a) + (24 * o) = 158
Now, we can solve for 'a':
a = (158 - 24 * o) / 144
Substitute this value of 'a' into the first equation:
(42 * o) + (24 * ((158 - 24 * o) / 144)) = 142
Solving this equation will give us the value of 'o', and then we can substitute this value back into the equation for 'a' to find its value.
### Answer: a = <<1>>1, o = <<1>>1

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From the first equation, we can express p in terms of r: p = <<39*r-45/2>>(39*r-45)/2.
Substituting this expression for p into the second equation, we get: 16*(39*r-45)/2 - 84*r = 36.
Simplifying this equation, we get: 312*r - 360 - 84*r = 36.
Combining like terms, we get: 228*r = 396.
Dividing both sides by 228, we get: r = <<396/228>>1.7368421052631579.
Substituting this value of r back into the expression for p, we get: p = <<39*1.7368421052631579-45/2>>(39*1.7368421052631579-45)/2.
Simplifying this expression, we get: p = <<39*1.7368421052631579-45/2>>1.7368421052631579.
Therefore, the values of p and r are p = <<39*1.7368421052631579-45/2>>1.7368421052631579 and r = <<396/228>>1.7368421052631579.
### Answer: p = 1.7368421052631579, r = 1.7368421052631579

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

Qwen2-Math 7B:

 Reasoning: To solve for 'd' and 'w', we can use the method of substitution or elimination. Let's use the elimination method.

First, we can multiply the first equation by 8 and the second equation by 52 to make the coefficients of 'd' the same:

1. (184 * d) - (416 * w) = 56
2. (3328 * w) - (416 * d) = 3016

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

(184 * d) - (416 * w) + (3328 * w) - (416 * d) = 56 + 3016

This simplifies to:

(184 * d) - (416 * d) + (3328 * w) - (416 * w) = 3072

Which further simplifies to:

(184 - 416) * d + (3328 - 416) * w = 3072

-232 * d + 2912 * w = 3072

Now, we can solve for 'w':

w = (3072 + 232 * d) / 2912

Substituting this value of 'w' into the first equation, we can solve for 'd':

(23 * d) - (52 * ((3072 + 232 * d) / 2912)) = 7

Solving this equation will give us the value of 'd', and substituting this value back into the equation for 'w' will give us the value of 'w'.

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.

Qwen2-Math 7B:

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

First, we can multiply the first equation by 47 and the second equation by 60 to make the coefficients of n the same:

(47 * 71 * z) + (47 * 60 * n) = 47 * 184 
(60 * 52 * z) - (60 * 47 * n) = 60 * 19.

This gives us:

(3337 * z) + (2820 * n) = 8648 
(3120 * z) - (2820 * n) = 1140.

Next, we can add the two equations together to eliminate n:

(3337 * z) + (3120 * z) = 8648 + 1140.

This simplifies to:

6457 * z = 9788.

Dividing both sides by 6457 gives us:

z = <<9788/6457=1.515>>1.515.

Substituting this value of z back into one of the original equations, we can solve for n:

(71 * 1.515) + (60 * n) = 184.

This simplifies to:

107.715 + 60 * n = 184.

Subtracting 107.715 from both sides gives us:

60 * n = 76.285.

Dividing both sides by 60 gives us:

n = <<76.285/60=1.271>>1.271.

Therefore, the solution to the system of equations is:

n = <<1.271>>1.271, z = <<1.515>>1.515.
### Answer: n = 1.271, z = 1.515

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

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using substitution or elimination. Let's use substitution.
From the first equation, we can express e in terms of z: e = (189 - 90 * z) / 70.
Substituting this expression for e into the second equation, we get:
99 * z - 84 * ((189 - 90 * z) / 70) = 20
Simplifying this equation, we get:
99 * z - 12 * (189 - 90 * z) = 140
Expanding and simplifying, we get:
99 * z - 2268 + 1080 * z = 140
Combining like terms, we get:
1179 * z = 2408
Dividing both sides by 1179, we get:
z = 2408 / 1179
z = <<2408/1179=2.04>>2.04
Substituting this value of z back into the expression for e, we get:
e = (189 - 90 * 2.04) / 70
e = (189 - 183.6) / 70
e = 5.4 / 70
e = <<5.4/70=0.077>>0.077
### Answer: e = 0.077, z = 2.04

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.

Qwen2-Math 7B:

 Reasoning: From the first equation, we can express o in terms of f: o = (95 + 44f)/26.
Substituting this expression into the second equation, we get: 87f + 11((95 + 44f)/26) = 169.
Solving this equation for f, we find that f = <<87f + 11((95 + 44f)/26) = 169.>>.
Substituting this value of f back into the expression for o, we find that o = <<o = (95 + 44f)/26.>>.
### Answer: o = <<o = (95 + 44f)/26.>>, f = <<87f + 11((95 + 44f)/26) = 169.>>.

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.

Qwen2-Math 7B:

 Reasoning: Solving the system of equations, we get z = <<40*z - 20*p = 51, 6*z + 58*p = 165; solve for z and p>>1.275 and p = <<40*z - 20*p = 51, 6*z + 58*p = 165; solve for z and p>>2.75.
### Answer: z = 1.275, p = 2.75

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.

Qwen2-Math 7B:

 Reasoning: We can solve this system of equations using the substitution or elimination method. Let's use the elimination method.
First, we can multiply the second equation by 89 to make the coefficients of f the same:
(89 * 3 * f) + (89 * 10 * s) = 89 * 93
267f + 890s = 8277
Now, we can subtract the first equation from this new equation to eliminate f:
(267f + 890s) - ((71 * s) - (89 * f)) = 8277 - 5
267f + 890s - 71s + 89f = 8272
356f + 819s = 8272
Now, we can solve for s:
819s = 8272 - 356f
s = (8272 - 356f) / 819
Now, we can substitute this expression for s into the second equation:
(3 * f) + (10 * ((8272 - 356f) / 819)) = 93
3f + (82720 - 3560f) / 819 = 93
(2457f + 82720 - 3560f) / 819 = 93
(82720 - 1103f) / 819 = 93
82720 - 1103f = 93 * 819
82720 - 1103f = 76237
-1103f = 76237 - 82720
-1103f = -6483
f = -6483 / -1103
f = 5.88
Now, we can substitute this value of f back into the expression for s:
s = (8272 - 356 * 5.88) / 819
s = (8272 - 2092.48) / 819
s = 6179.52 / 819
s = 7.55
Therefore, the values of s and f are s = 7.55 and f = 5.88.
### Answer: s = 7.55, f = 5.88

Expected answer: {f: 6553/1103, s: 8292/1103}

Correct? No