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

Llama 3 8B:

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

First, we can solve the second equation for s:

s = (121 - 12q) / 30

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

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

Simplify the equation:

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

Simplify further:

808/30 - 16q/30 - 91q = 37

Combine like terms:

(808 - 16 - 2730) / 30 - 91q = 37

Simplify:

-1862/30 - 91q = 37

Multiply both sides by 30 to eliminate the fraction:

-1862 - 2730q = 1110

Add 1862 to both sides:

-2730q = 2872

Divide both sides by -2730:

q = -2872 / 2730

q = -1.05

Now that we have the value of q, we can find the value of s:

s = (121 - 12(-1.05)) / 30

s = (121 + 12.6) / 30

s = 133.6 / 30

s = 4.45

### Answer: q = -1.05, s = 4.45

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.

Llama 3 8B:

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

First, we can solve the second equation for m:

79m - 6b = 48
79m = 6b + 48
m = (6b + 48) / 79

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

4b + 44((6b + 48) / 79) = 180

Multiply both sides by 79 to eliminate the fraction:

316b + 2112 = 14280

Subtract 2112 from both sides:

316b = 12168

Divide both sides by 316:

b = 12168 / 316
b = 38.5

Now that we have found b, we can substitute it back into one of the original equations to find m. We'll use the second equation:

79m - 6(38.5) = 48

Simplify:

79m - 231 = 48

Add 231 to both sides:

79m = 279

Divide both sides by 79:

m = 279 / 79
m = 3.5

### Answer: b = 38.5, m = 3.5

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

Correct? No

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

Llama 3 8B:

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

First, we will multiply both equations by necessary multiples such that the coefficients of o's in both equations are the same:

1) Multiply the first equation by 29:
42 * o - 15 * g = 28
29 * (42 * o - 15 * g) = 29 * 28
1162 * o - 435 * g = 812

2) Multiply the second equation by 15:
47 * o + 29 * g = 141
15 * (47 * o + 29 * g) = 15 * 141
705 * o + 435 * g = 2115

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

(705 * o + 435 * g) - (1162 * o - 435 * g) = 2115 - 812
-457 * o = 1303
o = -1303/457

Now that we have the value of o, substitute it into one of the original equations to find the value of g. We will use the first equation:

42 * o - 15 * g = 28
42 * (-1303/457) - 15 * g = 28
-1094/11 - 15 * g = 28
-1094/11 - 15 * g + 1094/11 = 28 + 1094/11
-15 * g = 140/11
g = -140/165

### Answer: o = -1303/457, g = -140/165

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.

Llama 3 8B:

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

First, we can simplify the first equation by distributing the multiplication:

12v - 6o = 21

Next, we can simplify the second equation by distributing the multiplication:

76v - 45o = 50

Now, we can try to eliminate one of the variables by multiplying the two equations by necessary multiples such that the coefficients of o's in both equations are the same. Let's multiply the first equation by 5 and the second equation by 6:

60v - 30o = 105
456v - 270o = 300

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

456v - 60v = 300 - 105
396v = 195

Now, we can solve for v:

v = 195 / 396
v = 0.5

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

12v - 6o = 21
12(0.5) - 6o = 21
6 - 6o = 21

Now, we can subtract 6 from both sides:

-6o = 15

Finally, we can divide both sides by -6 to solve for o:

o = -15 / 6
o = -2.5

### Answer: v = 0.5, o = -2.5

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.

Llama 3 8B:

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

First, we can solve the second equation for g:

90g = 143 - 2f
g = (143 - 2f) / 90

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

75f + 25((143 - 2f) / 90) = 138

Multiply both sides by 90 to eliminate the fraction:

675f + 25(143 - 2f) = 138 * 90

Expand and simplify:

675f + 3575 - 50f = 12420

Combine like terms:

625f = 8865

Divide by 625:

f = 8865 / 625
f = 14.24

Now that we have found f, we can find g by substituting f into the expression we found earlier:

g = (143 - 2(14.24)) / 90
g = (143 - 28.48) / 90
g = 114.52 / 90
g = 1.27

### Answer: f = 14.24, g = 1.27

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.

Llama 3 8B:

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

First, we can rewrite the second equation to isolate y:

79y = 65n - 7

Now, divide both sides by 79:

y = (65n - 7) / 79

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

194 = 4((65n - 7) / 79) + 14n

Multiply both sides by 79 to eliminate the fraction:

15244 = 260n - 28 + 14n

Combine like terms:

15244 = 274n - 28

Add 28 to both sides:

15272 = 274n

Divide both sides by 274:

n = 15272 / 274

n = 56

Now that we have found n, we can substitute it back into one of the original equations to find y. We'll use the second equation:

79y = 65(56) - 7

79y = 3643 - 7

79y = 3636

Divide both sides by 79:

y = 3636 / 79

y = 46

### Answer: y = 46, n = 56

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.

Llama 3 8B:

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

From the second equation, we can express l in terms of g:

6 = 41 * l - 53 * g
41 * l = 6 + 53 * g
l = (6 + 53 * g) / 41

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

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

Multiply both sides by 41 to eliminate the fraction:

6024 = 28 * 41 * g + 26 * (6 + 53 * g)

Expand and simplify:

6024 = 1148 * g + 156 + 1378 * g

Combine like terms:

6024 = 2516 * g + 156

Subtract 156 from both sides:

5868 = 2516 * g

Divide both sides by 2516:

g = 5868 / 2516
g = 2.33

Now that we have found g, we can find l by substituting g into one of the original equations. We'll use the second equation:

6 = 41 * l - 53 * g
6 = 41 * l - 53 * 2.33
6 = 41 * l - 123.69
41 * l = 6 + 123.69
41 * l = 129.69
l = 129.69 / 41
l = 3.18

### Answer: l = 3.18, g = 2.33

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.

Llama 3 8B:

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

First, we can multiply equation (1) by 7 and equation (2) by 56 to make the coefficients of y in both equations the same:

1) 140p + 392y = 630
2) 496p + 7y = 546

Now, we can subtract equation (2) from equation (1) to eliminate y:

(140p + 392y) - (496p + 7y) = 630 - 546
140p - 496p = 630 - 546 - 392y + 7y
-356p = 84
p = -84/356

Now that we have the value of p, we can substitute it into one of the original equations to find the value of y. Let's use equation (1):

20p + 56y = 90
20(-84/356) + 56y = 90
-1680/356 + 56y = 90
56y = 90 + 1680/356
56y = 90 + 48
56y = 138
y = 138/56
y = 123/48

So, the values of p and y are:

p = -84/356
y = 123/48

### Answer: p = -84/356, y = 123/48

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.

Llama 3 8B:

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

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

12*d + 138*k = 192

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

(12*d + 138*k) - (72*k - 22*d) = 192 - 17
12*d + 138*k - 72*k + 22*d = 192 - 17
34*d + 66*k = 175

Now we can solve for d:

34*d = 175 - 66*k
d = (175 - 66*k) / 34

Now we can substitute this expression for d into one of the original equations. Let's use the first equation:

72*k - 22*(175 - 66*k) / 34 = 17

Multiply both sides by 34 to eliminate the fraction:

2488*k - 22*(175 - 66*k) = 578

Expand and simplify:

2488*k - 3850 + 1452*k = 578
33340*k - 3850 = 578
33340*k = 4428

Now we can solve for k:

k = 4428 / 33340
k = 0.132

Now that we have the value of k, we can find the value of d:

d = (175 - 66*0.132) / 34
d = (175 - 8.712) / 34
d = 166.288 / 34
d = 4.89

So, the values of variables k and d are:

k = 0.132
d = 4.89

### Answer: k = 0.132, d = 4.89

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

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of d's in both equations are the same:

1) Multiply the first equation by 10:
730h - 330d = 480

2) Multiply the second equation by 33:
330d + 462h = 2973

Now, subtract the first equation from the second equation to eliminate the d term:

462h - 730h = 2973 - 480
-268h = 2493

Now, divide both sides by -268:

h = -2493/268
h = -9.25

Now that we have the value of h, substitute it into one of the original equations to find the value of d. We'll use the first equation:

73h - 33d = 48
73(-9.25) - 33d = 48
-675 - 33d = 48

Add 675 to both sides:

-33d = 723
d = -723/33
d = -22

So, the values of d and h are:

d = -22
h = -9.25

### Answer: d = -22, h = -9.25

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

Llama 3 8B:

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

First, we can multiply both equations by necessary multiples such that the coefficients of e's in both equations are the same:

1) 43q - 44e = 29
 Multiply equation (1) by 43 and equation (2) by 44:
172q - 1932e = 1253
132q + 1932e = 5720

Now, we can subtract equation (2) from equation (1) to eliminate e:

(172q - 132q) - (1932e - 1932e) = 1253 - 5720
40q = -4467

Now, divide by 40:

q = -4467/40
q = -111.675

Now that we have the value of q, we can substitute it into one of the original equations to find the value of e. We'll use equation (1):

43q - 44e = 29
43(-111.675) - 44e = 29
-4829.725 - 44e = 29

Add 4829.725 to both sides:

-44e = 4829.725 + 29
-44e = 4858.725

Divide by -44:

e = -4858.725/44
e = 110.205

### Answer: q = -111.675, e = 110.205

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))

Llama 3 8B:

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

First, we can solve the first equation for r:

r = (53 + 74a) / 89

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

109 = (37a + 6((53 + 74a) / 89))

Multiply both sides of the equation by 89 to eliminate the fraction:

9697 = 37a + 6(53 + 74a)

Expand and simplify the right-hand side:

9697 = 37a + 318 + 444a

Combine like terms:

9697 = 481a + 318

Subtract 318 from both sides:

9379 = 481a

Divide both sides by 481:

a = 9379 / 481

a = 19.5

Now that we have found a, we can substitute this value back into one of the original equations to find r. We'll use the first equation:

r = (53 + 74(19.5)) / 89

r = (53 + 1443) / 89

r = 1496 / 89

r = 16.8

### Answer: r = 16.8, a = 19.5

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.

Llama 3 8B:

Let's start by using the information from equation (2) to express the weight of 'q' in terms of 'g':

12q - 50g = 19

Now, we can use equation (1) to express the weight of 'g' in terms of 'q':

42g + 12q = 169

Substitute the expression for 'q' from equation (2) into equation (1):

42g + 12(19 + 50g) = 169

Expand and simplify:

42g + 228 + 600g = 169

Combine like terms:

642g = -59

Divide by 642:

g = -59/642

Now that we have the value of 'g', we can find the value of 'q' by substituting it into equation (2):

12q = 19 + 50(-59/642)

Simplify:

12q = -19

Divide by 12:

q = -19/12

### Answer: g = -59/642, q = -19/12

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

Llama 3 8B:

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

First, let's multiply both equations by necessary multiples such that the coefficients of v's in both equations are the same:

1) Multiply the first equation by 62:
37s - 11v = 54
37s - 11v = 54
148s - 62v = 332

2) Multiply the second equation by 11:
82s - 62v = 41
82s - 62v = 41
914s - 682v = 451

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

914s - 148s = 451 - 332
766s = 119

Now, divide by 766:

s = 119/766
s = 0.155

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

37s - 11v = 54
37(0.155) - 11v = 54
5.71 - 11v = 54

Add 11v to both sides:

5.71 = 54 + 11v
11v = 54 - 5.71
11v = 48.29

Divide by 11:

v = 48.29/11
v = 4.39

### Answer: s = 0.155, v = 4.39

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.

Llama 3 8B:

Let's solve the system of equations.

First, we can multiply the two equations by necessary multiples such that the coefficients of c's in both equations are the same:

1) Multiply the first equation by 48 and the second equation by 65:
48 * 41 * c + 65 * 48 * z = 151 * 48
65 * 78 * z - 65 * 48 * c = 65 * 48

2) Now, we can subtract the second equation from the first equation:
(48 * 41 - 65 * 48) * c = 151 * 48 - 65 * 48
-208 * c = 6048 - 65 * 48
-208 * c = 6048 - 65 * 48
-208 * c = 6048 - 3120
-208 * c = 2928
c = -2928/208
c = -14

Now that we have the value of c, we can substitute it into one of the original equations to find the value of z. We'll use the first equation:

41 * c + 65 * z = 151
41 * (-14) + 65 * z = 151
-574 + 65 * z = 151
65 * z = 725
z = 725/65
z = 11

### Answer: c = -14, z = 11

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?

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of c's in both equations are the same:

1) Multiply the first equation by 76 and the second equation by 91:

4560c - 6876i = 532
637i + 6968c = 13528

2) Subtract the first equation from the second equation to eliminate c:

637i + 6968c - (4560c - 6876i) = 13528 - 532
637i + 6968c - 4560c + 6876i = 13528 - 532
1197i = 13496

3) Divide both sides by 1197:

i = 13496/1197
i = 11.25

4) Now that we have the value of i, substitute it into one of the original equations to find the value of c. We'll use the first equation:

60c - 91(11.25) = 7
60c - 1031.25 = 7
60c = 1031.25 + 7
60c = 1038.25
c = 1038.25/60
c = 17.305

### Answer: c = 17.305, i = 11.25

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

Llama 3 8B:

Let's solve the system of linear equations.

We can solve the first equation for v:

v = (69 + 37*e) / 71

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

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

Multiply both sides by 71 to eliminate the fraction:

2871*e + 10676 = 12964

Subtract 12964 from both sides:

2871*e = 2288

Divide both sides by 2871:

e = 2288 / 2871

e ≈ 0.80

Now that we have found e, we can find v by substituting e back into one of the original equations. We'll use the first equation:

71*v - 37*0.80 = 69

71*v - 29.6 = 69

Add 29.6 to both sides:

71*v = 98.6

Divide both sides by 71:

v = 98.6 / 71

v ≈ 1.39

### Answer: e ≈ 0.80, v ≈ 1.39

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.

Llama 3 8B:

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

From the first equation, we can write:

25v + 69d = 113

From the second equation, we can write:

26d + 42v = 85

Now, we can multiply the first equation by 2 and the second equation by 1 to make the coefficients of 'd' the same:

50v + 138d = 226
26d + 42v = 85

Subtract the second equation from the first equation to eliminate 'v':

138d - 26d = 226 - 85
112d = 141

Now, divide both sides by 112:

d = 141/112
d = 1.265625

Now that we have the value of 'd', we can substitute it into one of the original equations to find the value of 'v'. We'll use the first equation:

25v + 69(1.265625) = 113

Simplify the right-hand side:

25v + 88.4375 = 113

Subtract 88.4375 from both sides:

25v = 24.5625

Divide both sides by 25:

v = 24.5625/25
v = 0.9825

### Answer: d = 1.265625, v = 0.9825

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

Llama 3 8B:

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

First, we can multiply both sides of the first equation by 91 to get:

3917z - 8281g = 2973

Now, we can multiply both sides of the second equation by 3 to get:

216g - 9z = 204

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

3917z - 8281g + 216g - 9z = 2973 + 204

Combine like terms:

3908z - 8065g = 3177

Now, we can divide both sides by 3908 to get:

z = (3177 + 8065g) / 3908

Now, substitute this expression for z into one of the original equations. Let's use the first equation:

43z - 91g = 33

Substitute the expression for z:

43((3177 + 8065g) / 3908) - 91g = 33

Multiply both sides by 3908 to eliminate the fraction:

16141 + 34835g - 8281g = 12916

Combine like terms:

-4806g = -3215

Divide both sides by -4806:

g = 3215 / 4806

g = 0.668

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

43z - 91g = 33

Substitute the value of g:

43z - 91(0.668) = 33

Multiply both sides by 100 to eliminate the decimal:

4300z - 9132 = 3300

Add 9132 to both sides:

4300z = 9432

Divide both sides by 4300:

z = 9432 / 4300

z = 2.2

### Answer: g = 0.668, z = 2.2

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.

Llama 3 8B:

Let's solve the system of equations.

First, we can multiply both sides of the second equation by 12 to make the coefficients of f equal:

432c - 252f = 408

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

432c - 50c - 252f + 12f = 408 - 92
382c = 316

Now, we can divide both sides by 382 to solve for c:

c = 316/382
c = 8

Now that we have found c, we can substitute it into one of the original equations to find f. We'll use the first equation:

50c + 12f = 92
50(8) + 12f = 92
400 + 12f = 92

Subtract 400 from both sides:

12f = -308

Divide both sides by -12:

f = 308/12
f = 25.67

Since f cannot be a fraction, we can round it to the nearest whole number. In this case, f = 26.

### Answer: c = 8, f = 26.

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

Llama 3 8B:

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

First, we can solve the first equation for u:

u = (7 + 75d) / 87

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

85d - 82((7 + 75d) / 87) = 54

Multiply both sides of the equation by 87 to eliminate the fraction:

7535d - 82(7 + 75d) = 4716

Expand and simplify:

7535d - 574 - 6150d = 4716

Combine like terms:

-8615d = -1028

Divide both sides by -8615:

d = 1028 / 8615

d = 0.12

Now that we have found d, we can substitute this value back into one of the original equations to find u. We'll use the first equation:

87u - 75(0.12) = 7

87u - 9 = 7

Add 9 to both sides:

87u = 16

Divide both sides by 87:

u = 16 / 87

u = 0.184

### Answer: u = 0.184, d = 0.12.

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?

Llama 3 8B:

Let's start by solving the first equation:

(75 * a) - (4 * i) = 42

We can add (4 * i) to both sides to get:

(75 * a) = 42 + (4 * i)

Now, we can subtract 42 from both sides to get:

75a = 42 + 4i

Next, we can subtract 4i from both sides to get:

75a - 4i = 42

Now, we can divide both sides by 75 to get:

a - (4/75)i = 42/75

Now, let's move on to the second equation:

(10 * i) + (13 * a) = 160

We can subtract (13 * a) from both sides to get:

(10 * i) = 160 - (13 * a)

Now, we can divide both sides by 10 to get:

i = (160 - 13a) / 10

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

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

We can multiply both sides by 10 to get rid of the fraction:

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

Now, we can expand the right-hand side:

(750 * a) - 640 + 52a = 420

Now, we can add 640 to both sides to get:

(750 * a) + 52a = 1060

Now, we can combine like terms:

802a = 1060

Now, we can divide both sides by 802 to get:

a = 1060/802

a = 1.32

Now that we have found a, we can substitute it into one of the original equations to find i. Let's use the second equation:

(10 * i) + (13 * 1.32) = 160

We can simplify the right-hand side:

(10 * i) + 17.16 = 160

Now, we can subtract 17.16 from both sides to get:

(10 * i) = 142.84

Now, we can divide both sides by 10 to get:

i = 14.284

So, the values of i and a are:

i = 14.284
a = 1.32

### Answer: i = 14.284, a = 1.32

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

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of p's in both equations are the same:

1) Multiply the first equation by 18:
666p + 1332c = 3276
2) Multiply the second equation by 74:
198c - 324p = 962

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

666p + 1332c - (198c - 324p) = 3276 - 962
666p + 1332c - 198c + 324p = 2314
690p + 1134c = 2314

Now, we can solve for p:

690p = 2314 - 1134c
p = (2314 - 1134c) / 690

Now, substitute the expression for p into one of the original equations, say the first equation:

37 * ((2314 - 1134c) / 690) + 74c = 183

Simplify the equation:

37 * (2314 - 1134c) / 690 + 74c = 183
1373 - 4263c / 19 + 74c = 183

Multiply both sides by 19 to eliminate the fraction:

26067 - 4263c + 1414c = 3483
12494 - 285c = 3483

Now, subtract 3483 from both sides:

12494 - 285c - 3483 = 0
90011 - 285c = 0

Now, divide both sides by -285:

c = 90011 / 285
c = 316

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

p = (2314 - 1134c) / 690
p = (2314 - 1134 * 316) / 690
p = (2314 - 357624) / 690
p = -356310 / 690
p = -516

### Answer: p = -516, c = 316

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.

Llama 3 8B:

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

First, we can solve the first equation for k:

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

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

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

Multiply both sides by 48 to eliminate the fraction:

768p + 33(30p + 37) = 5040

Expand and simplify:

768p + 990p + 1217 = 5040
2058p + 1217 = 5040

Subtract 1217 from both sides:

2058p = 3823

Divide both sides by 2058:

p = 3823 / 2058
p = 1.86 (approximately)

Now that we have found p, we can substitute it back into one of the original equations to find k. We'll use the first equation:

48k - 30p = 37
48k - 30(1.86) = 37

Multiply 30(1.86) = 56.8:

48k - 56.8 = 37

Add 56.8 to both sides:

48k = 93.8

Divide both sides by 48:

k = 93.8 / 48
k = 1.96 (approximately)

So, the values of k and p are approximately:

k ≈ 1.96
p ≈ 1.86

### Answer: k ≈ 1.96, p ≈ 1.86.

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.

Llama 3 8B:

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

First, let's multiply equation (1) by 46 to make the coefficients of f in both equations the same:

46(75v - 69f = 14)
3465v - 3186f = 686

Now, add equation (2) to the modified equation (1):

3465v - 3186f = 686
46f + 53v = 110
-------------------
3511v - 3186f = 796

Now, divide both sides by -3186:

v = (796 + 3186f) / 3511

Substitute this expression for v into one of the original equations, say equation (1):

75((796 + 3186f) / 3511) - 69f = 14

Multiply both sides by 3511 to eliminate the fraction:

267750 + 239610f - 47565f = 15186

Combine like terms:

219285 + 960f = 15186

Subtract 219285 from both sides:

960f = -70799

Divide both sides by -960:

f = 73.75

Now that we have found f, we can find v by substituting f into the expression we found earlier:

v = (796 + 3186(73.75)) / 3511
v = (796 + 23625) / 3511
v = 24021 / 3511
v = 6.85

### Answer: v = 6.85, f = 73.75

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.

Llama 3 8B:

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

First, we can solve the second equation for g:

g = (37 + 70o) / 89

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

7o + 13((37 + 70o) / 89) = 131

Multiply both sides by 89 to eliminate the fraction:

637o + 13(37 + 70o) = 11693

Expand and simplify:

637o + 481 + 910o = 11693

Combine like terms:

1547o = 11112

Divide both sides by 1547:

o = 11112 / 1547

o = 7.2

Now that we have found o, we can find g by substituting o into one of the original equations. We'll use the second equation:

89g - 70(7.2) = 37

89g - 504 = 37

Add 504 to both sides:

89g = 541

Divide both sides by 89:

g = 541 / 89

g = 6.1

### Answer: o = 7.2, g = 6.1

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

Correct? No

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

Llama 3 8B:

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

First, we can multiply both equations by necessary multiples such that the coefficients of d's in both equations are the same:

1) Multiply the first equation by 11:
968d - 660k = 418
2) Multiply the second equation by 60:
1980k - 660d = 2760

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

(1980k - 660d) - (968d - 660k) = 2760 - 418
1980k - 660d - 968d + 660k = 2342
2012k - 1320d = 2342

Now, we can solve for k:

k = (2342 + 1320d) / 2012

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

88d - 60((2342 + 1320d) / 2012) = 38

Multiply both sides by 2012 to eliminate the fraction:

176,960d - 140,320 = 76,544

Now, subtract 76,544 from both sides:

176,960d = 64,416

Now, divide both sides by 176,960:

d = 64,416 / 176,960
d = 0.364

Now that we have the value of d, we can find the value of k:

k = (2342 + 1320d) / 2012
k = (2342 + 1320(0.364)) / 2012
k = (2342 + 480.48) / 2012
k = 2822.48 / 2012
k = 1.405

### Answer: d = 0.364, k = 1.405

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of y's in both equations are the same:

1) Multiply the first equation by 41 (which is the coefficient of y in the second equation):
24z + 72y = 139
41(24z + 72y) = 41(139)
576z + 2952y = 5671

2) Multiply the second equation by 1 (no need to multiply):
2z + 82y = 96

Now, subtract the second equation from the first equation:

(576z + 2952y) - (2z + 82y) = 5671 - 96
574z + 2870y = 5575

Now, simplify the equation:

574z = 5575 - 2870y
z = (5575 - 2870y) / 574

Now, substitute the value of z in one of the original equations. We'll use the first equation:

24z + 72y = 139
24((5575 - 2870y) / 574) + 72y = 139

Simplify the equation:

13920 - 103800y + 72y = 139
13920 - 103728y = 139
103728y = 13920 + 139
103728y = 13959
y = 13959 / 103728
y ≈ 0.134

Now that we have the value of y, we can find the value of z:

z = (5575 - 2870y) / 574
z = (5575 - 2870(0.134)) / 574
z = (5575 - 383.32) / 574
z = 5191.68 / 574
z ≈ 9.03

### Answer: y ≈ 0.134, z ≈ 9.03

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.

Llama 3 8B:

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

First, we can rewrite the equations in a more convenient form:

1) 87o - 29v = 1
2) 8v + 30o = 91

Now, we can solve the first equation for o:

o = (1 + 29v) / 87

Substitute this expression for o into the second equation:

8v + 30((1 + 29v) / 87) = 91

Multiply both sides by 87 to eliminate the fraction:

8v * 87 + 30(1 + 29v) = 91 * 87

Expand and simplify:

696v + 30 + 870v = 7937

Combine like terms:

1566v + 30 = 7937

Subtract 30 from both sides:

1566v = 7907

Divide both sides by 1566:

v = 7907 / 1566

v = 5

Now that we have found v, we can find o by substituting v into one of the original equations. We'll use the first equation:

o = (1 + 29(5)) / 87

o = (1 + 145) / 87

o = 146 / 87

o = 2

So, the values of v and o are:

v = 5
o = 2

### Answer: v = 5, o = 2

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.

Llama 3 8B:

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

First, we can simplify the first equation by multiplying both sides by 1 to get rid of the parentheses:

23h - 46p = 58

Next, we can simplify the second equation by multiplying both sides by 1 to get rid of the parentheses:

11p + 23h = 124

Now, we can solve for h in the first equation:

23h = 58 + 46p

Divide both sides by 23:

h = (58 + 46p) / 23

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

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

Simplify the equation:

11p + 58 + 46p = 124

Combine like terms:

57p + 58 = 124

Subtract 58 from both sides:

57p = 66

Divide both sides by 57:

p = 66 / 57

p = 1.16 (approximately)

Now that we have found p, we can substitute it back into one of the original equations to find h. We'll use the first equation:

23h - 46(1.16) = 58

Simplify:

23h - 53.36 = 58

Add 53.36 to both sides:

23h = 111.36

Divide both sides by 23:

h = 111.36 / 23

h = 4.84 (approximately)

### Answer: h ≈ 4.84, p ≈ 1.16.

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.

Llama 3 8B:

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

First, we can multiply equation (2) by 2 to make the coefficients of f in both equations the same:

2) 180d - 84f = 138

Now, we can add equation (1) and equation (2) to eliminate the f term:

(19d + 6f = 120) + (180d - 84f = 138)

This gives us:

199d = 258

Now, we can solve for d:

d = 258/199 = 1.3 (not an integer, so we'll try to eliminate the fraction)

d = 129/99 = 1 1/3 (not an integer, so we'll try to eliminate the fraction)

d = 128/98 = 1 1/7 (not an integer, so we'll try to eliminate the fraction)

d = 127/97 = 1 1/9 (not an integer, so we'll try to eliminate the fraction)

d = 126/96 = 1 1/2 (integer!)

So, d = 1 1/2 = 3/2 = 1.5 (not an integer, so we'll try to eliminate the fraction)

d = 1

Now that we have the value of d, we can substitute it into one of the original equations to solve for f. We'll use equation (1):

19d + 6f = 120

19(1) + 6f = 120

6f = 120 - 19 = 101

f = 101/6 = 16 5/6 (not an integer, so we'll try to eliminate the fraction)

f = 16

So, the values of d and f are:

d = 1
f = 16

### Answer: d = 1, f = 16.

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'?

Llama 3 8B:

Let's solve the system of linear equations step by step.

First, we can multiply equation (1) by 2 and equation (2) by 1 to make the coefficients of 'r' in both equations the same:

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

Now, we can subtract equation (2) from equation (1) to eliminate 'm':

(84 * m + 110 * r) - (66 * m - 52 * r) = 254 - 44
84 * m + 110 * r - 66 * m + 52 * r = 210
18 * m + 162 * r = 210

Next, we can subtract 162 * r from both sides to get:

18 * m = 210 - 162 * r
18 * m = 48 - 162 * r

Now, we can divide both sides by 18 to solve for 'm':

m = (48 - 162 * r) / 18

Now that we have the expression for 'm', we can substitute it into one of the original equations to solve for 'r'. Let's use equation (1):

42 * m + 55 * r = 127
42 * ((48 - 162 * r) / 18) + 55 * r = 127

Simplifying the equation, we get:

24 + 55 * r = 127
55 * r = 103
r = 103 / 55
r = 1.87

Now that we have the value of 'r', we can substitute it back into the expression for 'm' to find the value of 'm':

m = (48 - 162 * 1.87) / 18
m = (48 - 303.54) / 18
m = -255.54 / 18
m = -14.23

### Answer: m = -14.23, r = 1.87

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

Llama 3 8B:

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

First, we will multiply the two equations by necessary multiples such that the coefficients of n's in both equations are the same:

1) Multiply the first equation by 71 and the second equation by 31:

2177n + 4480w = 8480
1771w + 5041n = 5373

2) Subtract the second equation from the first equation to eliminate n:

4480w - 1771w = 8480 - 5373
2711w = 3107

3) Divide both sides by 2711:

w = 3107/2711
w = 1.15

4) Now that we have the value of w, substitute it into one of the original equations to find the value of n. We will use the first equation:

31n + 64(1.15) = 120

5) Simplify the equation:

31n + 76.4 = 120

6) Subtract 76.4 from both sides:

31n = 43.6

7) Divide both sides by 31:

n = 43.6/31
n = 1.41

### Answer: n = 1.41, w = 1.15.

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.

Llama 3 8B:

Let's solve the system of linear equations step by step.

We have two equations:

1) 72a + 26u = 112
2) 76u - 77a = 31

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

First, we can multiply equation (1) by 77 and equation (2) by 72 to make the coefficients of a in both equations the same:

1) 5548a + 1972u = 8656
2) 5472u - 5516a = 2184

Now, we can subtract equation (2) from equation (1) to eliminate a:

(5548a + 1972u) - (5472u - 5516a) = 8656 - 2184
5548a + 1972u - 5472u + 5516a = 8656 - 2184
11064a = 6472

Now, we can solve for a:

a = 6472 / 11064
a = 0.58

Now that we have the value of a, we can substitute it into one of the original equations to solve for u. Let's use equation (1):

72a + 26u = 112
72(0.58) + 26u = 112
41.76 + 26u = 112

Subtract 41.76 from both sides:

26u = 70.24

Divide both sides by 26:

u = 70.24 / 26
u = 2.7

### Answer: u = 2.7, a = 0.58

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of b's in both equations are the same:

1) Multiply the first equation by 93:
93(54n + 18b = 143) => 5493n + 1674b = 13331

2) Multiply the second equation by 18:
18(87n - 93b = 48) => 1566n - 1674b = 864

Now, we can subtract the second equation from the first equation to eliminate the term with b:

(5493n + 1674b = 13331) - (1566n - 1674b = 864)
=> 6937n = 12467

Now, we can solve for n:
6937n = 12467
n = 12467/6937
n = 1.8

Now that we have the value of n, we can substitute it into one of the original equations to find the value of b. We'll use the first equation:

54n + 18b = 143
54(1.8) + 18b = 143
97.2 + 18b = 143

Subtract 97.2 from both sides:
18b = 45.8

Divide both sides by 18:
b = 45.8/18
b = 2.55

### Answer: b = 2.55, n = 1.8

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)?

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of p's in both equations are the same:

1) Multiply the first equation by 88:
53 * e + 7 * p = 103
53 * e + 7 * p = 103
88 * 53 * e + 88 * 7 * p = 88 * 103

2) Multiply the second equation by 7:
69 * e - 88 * p = 6
7 * 69 * e - 7 * 88 * p = 7 * 6

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

(88 * 53 * e + 88 * 7 * p) - (7 * 69 * e - 7 * 88 * p) = (88 * 103) - (7 * 6)
88 * 53 * e + 88 * 7 * p - 7 * 69 * e + 7 * 88 * p = 88 * 103 - 7 * 6
(88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6 + 88 * 7 * p - 7 * 88 * p
(88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6 + 88 * (7 * p - 7 * p)
(88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6 + 88 * 0
(88 * 53 - 7 * 69) * e = 88 * 103 - 7 * 6
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103 - 42
(88 * 53 - 7 * 69) * e = 88 * 103

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.

Llama 3 8B:

Let's solve the system of linear equations.

First, we can multiply the first equation by 24 to make the coefficients of p in both equations the same:

24((18 * p) - (7 * s)) = 24 * 21
432p - 168s = 504

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

432p - 168s = 504
-(51s - 24p) = 14

Combine like terms:

432p - 168s - 51s + 24p = 504 - 14
432p - 219s = 490

Now, we can solve for p:

432p = 490 + 219s
p = (490 + 219s) / 432

Now, substitute this expression for p into the original first equation:

((18 * ((490 + 219s) / 432)) - (7 * s)) = 21

Simplify and solve for s:

(18 * (490 + 219s) / 432) - 7s = 21
(1710 + 3918s) / 432 - 7s = 21
3918s - 7s = 21 * 432 - 1710
3911s = 9261 - 1710
3911s = 7551
s = 7551 / 3911
s = 1.94 (approximately)

Now that we have the value of s, we can find the value of p:

p = (490 + 219 * 1.94) / 432
p = (490 + 423.66) / 432
p = 913.66 / 432
p = 2.11 (approximately)

### Answer: p ≈ 2.11, s ≈ 1.94.

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.

Llama 3 8B:

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

We have two equations:

1) 59c - 34w = 84
2) 11c + 42w = 98

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

First, we'll multiply both equations by necessary multiples such that the coefficients of w's in both equations are the same:

1) 59c - 34w = 84
 Multiply equation (1) by 3 and equation (2) by 2:
3(59c - 34w = 84) => 177c - 102w = 252
2) 11c + 42w = 98
 Multiply equation (2) by 3:
3(11c + 42w = 98) => 33c + 126w = 294

Now, subtract equation (2) from equation (1):

(177c - 102w = 252) - (33c + 126w = 294)
=> 144c - 228w = -42

Now, we have a new equation:

144c - 228w = -42

Now, we'll multiply equation (1) by 1 and equation (2) by 2:
1(59c - 34w = 84) => 59c - 34w = 84
2(11c + 42w = 98) => 22c + 84w = 196

Now, add equation (1) and equation (2):

(59c - 34w = 84) + (22c + 84w = 196)
=> 81c + 50w = 280

Now, we have a new equation:

81c + 50w = 280

Now, we'll solve the system of equations by solving the above two equations:

144c - 228w = -42
81c + 50w = 280

Now, multiply equation (2) by 3:
3(81c + 50w = 280) => 243c + 150w = 840

Now, subtract equation (1) from equation (2):

(243c + 150w = 840) - (144c - 228w = -42)
=> 387c + 378w = 882

Now, divide both sides by 387:
c = 882/387
c = 2.28

Now, substitute the value of c in one of the original equations, say equation (1):

59c - 34w = 84
59(2.28) - 34w = 84
133.32 - 34w = 84

Now, subtract 133.32 from both sides:
-34w = -49.32

Now, divide both sides by -34:
w = 49.32/34
w = 1.45

### Answer: c = 2.28, w = 1.45

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of f's in both equations are the same:

1) Multiply the first equation by 42 and the second equation by 45:

1) 1890f + 1764z = 4282
2) 2700z - 1890f = 585

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

1890f + 1764z = 4282
- (2700z - 1890f = 585)

This gives us:

3800z = 3697

Now, we can solve for z:

z = 3697/3800
z = 0.9755

Now that we have the value of z, we can substitute it into one of the original equations to solve for f. We'll use the first equation:

45f + 42z = 101
45f + 42(0.9755) = 101

Simplifying the equation:

45f + 41.71 = 101

Subtracting 41.71 from both sides:

45f = 59.29

Dividing both sides by 45:

f = 59.29/45
f = 1.315

### Answer: f = 1.315, z = 0.9755

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.

Llama 3 8B:

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

First, we can solve the first equation for p:

26p - 21u = 6
26p = 6 + 21u
p = (6 + 21u) / 26

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

15((6 + 21u) / 26) + 58u = 83

Multiply both sides by 26 to eliminate the fraction:

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

Expand and simplify:

90 + 315u + 1492u = 2158

Combine like terms:

2507u = 2068

Divide by 2507:

u = 2068 / 2507
u = 0.826

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

26p - 21u = 6
26p - 21(0.826) = 6

Simplify:

26p - 17.346 = 6

Add 17.346 to both sides:

26p = 23.346

Divide by 26:

p = 23.346 / 26
p = 0.900

### Answer: p = 0.900, u = 0.826.

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

Llama 3 8B:

Let's solve the system of equations.

We can start by multiplying equation (1) by 8 and equation (2) by 38 to make the coefficients of s in both equations the same:

1) 736n - 304s = 496
2) 2236n + 304s = 2860

Now, we can subtract equation (1) from equation (2) to eliminate the s term:

2236n - 736n = 2860 - 496
1500n = 2364

Now, we can solve for n:

n = 2364/1500
n = 1.576

Now that we have the value of n, we can substitute it into one of the original equations to solve for s. We'll use equation (1):

92n - 38s = 62
92(1.576) - 38s = 62
148.352 - 38s = 62

Now, we can solve for s:

-38s = -86.352
s = 86.352/38
s = 2.272

### Answer: n = 1.576, s = 2.272

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.

Llama 3 8B:

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

We have:

1) 87z - 35e = 63
2) 81z + 58e = 154

First, we can multiply equation (1) by 58 and equation (2) by 35 to make the coefficients of e in both equations the same:

1) 5049z - 1990e = 3633
2) 2835z + 2030e = 5390

Now, we can subtract equation (1) from equation (2) to eliminate the e term:

2835z + 2030e - 5049z + 1990e = 5390 - 3633
-2814z = 3407

Now, divide both sides by -2814:

z = -3407/2814

Now that we have the value of z, we can substitute it into one of the original equations to find the value of e. We'll use equation (1):

87z - 35e = 63
87(-3407/2814) - 35e = 63

Simplify:

-29919/2814 - 35e = 63

Multiply both sides by -2814 to eliminate the fraction:

29919 + 2814(35e) = -2814(63)

Simplify:

29919 + 123150e = -18486

Subtract 29919 from both sides:

123150e = -48405

Divide both sides by 123150:

e = -48405/123150

### Answer: z = -3407/2814, e = -48405/123150

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.

Llama 3 8B:

Let's solve the system of simultaneous linear equations.

We have two equations:

1) 11t + 44h = 110
2) 98t - 36h = 18

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

First, we can multiply equation (1) by 3 and equation (2) by 1 to make the coefficients of h in both equations the same:

1) 33t + 132h = 330
2) 98t - 36h = 18

Now, we can subtract equation (2) from equation (1) to eliminate h:

(33t + 132h) - (98t - 36h) = 330 - 18
33t + 132h - 98t + 36h = 312
-65t + 168h = 312

Now, we can solve for t:

-65t = 312 - 168h
t = (312 - 168h) / -65

Now that we have the value of t, we can substitute it into one of the original equations to solve for h. Let's use equation (1):

11t + 44h = 110
11((312 - 168h) / -65) + 44h = 110

Simplifying the equation:

-66 + 44h + 44h = 110
88h = 176
h = 176 / 88
h = 2

Now that we have the values of h and t, we can substitute them back into the original equations to verify:

1) 11t + 44h = 110
11(312/65) + 44(2) = 110
44 + 88 = 132 ≠ 110 (Error)

2) 98t - 36h = 18
98(312/65) - 36(2) = 18
176 - 72 = 104 ≠ 18 (Error)

It seems that there is an error in the system of equations. The values of h and t do not satisfy both equations.

### Answer: No solution exists.

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.

Llama 3 8B:

Let's solve the system of linear equations step by step.

First, we can rewrite the equations in standard form:

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

Next, we can multiply Equation 1 by 41 and Equation 2 by 50 to make the coefficients of o in both equations the same:

Equation 1 (multiplied by 41): 2789b - 2050o = 2265
Equation 2 (multiplied by 50): 2050o + 900b = 4250

Now, we can subtract Equation 1 from Equation 2 to eliminate the o variable:

(2050o + 900b) - (2789b - 2050o) = 4250 - 2265
900b - 2789b = 4250 - 2265
-1891b = 1985

Now, we can solve for b:

-1891b = -1985
b = 1985 / 1891
b ≈ 1.05

Now that we have the value of b, we can substitute it into one of the original equations to solve for o. We'll use Equation 1:

69b - 50o = 55
69(1.05) - 50o = 55
73.5 - 50o = 55

Now, we can solve for o:

-50o = -18.5
o = 18.5 / 50
o ≈ 0.37

So, the values of b and o are approximately 1.05 and 0.37, respectively.

### Answer: b ≈ 1.05, o ≈ 0.37

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of p's in both equations are the same:

1) Multiply the first equation by 5 and the second equation by 80:
5 * (67 * q - 80 * p = 65) => 335q - 400p = 325
80 * (6 * q + 5 * p = 177) => 480q + 400p = 14160

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

(480q + 400p = 14160) - (335q - 400p = 325)
=> 145q = 14035

Now, we can solve for q:
q = 14035 / 145
q = 96.69 (approximately)

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

67 * q - 80 * p = 65
67 * 96.69 - 80 * p = 65
6493.23 - 80 * p = 65

Now, we can solve for p:
p = (6493.23 - 65) / 80
p = 62.69 (approximately)

So, the values of p and q are approximately 62.69 and 96.69, respectively.

### Answer: p ≈ 62.69, q ≈ 96.69.

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.

Llama 3 8B:

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

First, we can solve the first equation for k:

10k + 48f = 161
10k = 161 - 48f
k = (161 - 48f) / 10

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

33((161 - 48f) / 10) - 41f = 31

Multiply both sides by 10 to eliminate the fraction:

330 - 1488f + 41f = 310

Combine like terms:

-1447f = -20

Divide both sides by -1447:

f = 20/1447

Now that we have found f, we can substitute this value back into one of the original equations to find k. We'll use the first equation:

10k + 48(20/1447) = 161

Multiply both sides by 1447 to eliminate the fraction:

14470k + 9600 = 233,332

Subtract 9600 from both sides:

14470k = 225,732

Divide both sides by 14470:

k = 225,732 / 14470

k = 15.6

So, the values of k and f that satisfy the system of equations are:

k = 15.6
f = 20/1447

### Answer: k = 15.6, f = 20/1447.

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

Llama 3 8B:

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

First, we can rewrite the first equation as:

n = 58l - 31

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

103 = (58l - 31) + 73l

Combine like terms:

103 = 131l - 31

Add 31 to both sides:

134 = 131l

Divide both sides by 131:

l = 134/131

l = 1.02

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

n = 58l - 31
n = 58(1.02) - 31
n = 59.24 - 31
n = 28.24

So, the values of l and n are:

l = 1.02
n = 28.24

### Answer: l = 1.02, n = 28.24

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

Llama 3 8B:

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

First, we will multiply the two equations by necessary multiples such that the coefficients of j's in both equations are the same:

1) Multiply the first equation by 37 and the second equation by 28:

1117y - 1036j = 1431
700y + 1036j = 3248

2) Now, subtract the first equation from the second equation to eliminate j:

700y - 1117y = 3248 - 1431
-417y = 1817

3) Now, divide both sides by -417:

y = -1817/417
y = -4.33

4) Now that we have the value of y, substitute it in one of the original equations to find the value of j. We will use the first equation:

29y - 28j = 39
29(-4.33) - 28j = 39

5) Simplify and solve for j:

-125.97 - 28j = 39
-28j = 39 + 125.97
-28j = 165.97
j = -165.97/28
j = -5.89

### Answer: y = -4.33, j = -5.89

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.

Llama 3 8B:

Let's solve the system of equations.

We can start by multiplying the first equation by 17 and the second equation by 85 to make the coefficients of a the same:

1) 1592u - 1425a = 1262
2) 8160u + 1445a = 15830

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

8160u - 1592u = 15830 - 1262
6568u = 14568

Now, we can divide both sides by 6568 to solve for u:

u = 14568/6568
u = 2.22

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

93u - 85a = 74
93(2.22) - 85a = 74
209.46 - 85a = 74

Now, we can subtract 74 from both sides and then divide both sides by -85 to solve for a:

-85a = -135.46
a = 135.46/85
a = 1.6

### Answer: u = 2.22, a = 1.6

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

Llama 3 8B:

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

First, we'll multiply both equations by necessary multiples such that the coefficients of g's in both equations are the same:

1) Multiply the first equation by 23:
97u - 61g = 15
 Multiply by 23:
2237u - 1387g = 345

2) Multiply the second equation by 61:
85u + 23g = 186
 Multiply by 61:
5175u + 1387g = 11346

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

5175u + 1387g - 2237u + 1387g = 11346 - 345
2948u = 11001

Now, divide by 2948:
u = 11001/2948
u = 3.73

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

97u - 61g = 15
97(3.73) - 61g = 15
365.21 - 61g = 15

Add 61g to both sides:
365.21 = 15 + 61g

Subtract 15 from both sides:
350.21 = 61g

Divide by 61:
g = 350.21/61
g = 5.74

### Answer: u = 3.73, g = 5.74

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.

Llama 3 8B:

Let's solve the system of equations.

We can rewrite the system as:

1) 17r + 67b = 103
2) 85r + 67b = 187

Subtracting equation (1) from equation (2), we get:

(85r - 17r) + (67b - 67b) = 187 - 103
68r = 84

Dividing both sides by 68, we get:

r = 84/68
r = 1.25

Now that we have the value of r, we can substitute it into one of the original equations to solve for b. Let's use equation (1):

17r + 67b = 103
17(1.25) + 67b = 103
17.25 + 67b = 103

Subtracting 17.25 from both sides, we get:

67b = 85.75

Dividing both sides by 67, we get:

b = 85.75/67
b = 1.28

### Answer: r = 1.25, b = 1.28

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.

Llama 3 8B:

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

From equation (1), we can express n in terms of t:

n = (41 + 54t) / 85

Now, substitute this expression for n into equation (2):

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

Simplify the equation:

38t + (1230 + 1620t) / 85 = 126

Multiply both sides by 85 to eliminate the fraction:

3230 + 1620t = 10750

Subtract 3230 from both sides:

1620t = 7530

Divide both sides by 1620:

t = 7530 / 1620

t = 4.67

Now that we have the value of t, we can find the value of n:

n = (41 + 54(4.67)) / 85

n = (41 + 253.58) / 85

n = 294.58 / 85

n = 3.47

### Answer: t = 4.67, n = 3.47

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.

Llama 3 8B:

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

Equation 1: 75u - 69q = 5

Equation 2: 48u + 25q = 140

We can solve Equation 1 for u:

u = (5 + 69q) / 75

Now, substitute this expression for u into Equation 2:

48((5 + 69q) / 75) + 25q = 140

Multiply both sides by 75 to eliminate the fraction:

288 + 1032q + 1875q = 10500

Combine like terms:

3007q = 10500 - 288

q = (10500 - 288) / 3007

q ≈ 3.48

Now that we have found q, we can substitute it back into Equation 1 to find u:

u = (5 + 69(3.48)) / 75

u ≈ 1.14

### Answer: u ≈ 1.14, q ≈ 3.48

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.

Llama 3 8B:

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

First, we can solve the first equation for v:

20v + 17x = 149

Subtract 17x from both sides:

20v = 149 - 17x

Divide both sides by 20:

v = (149 - 17x) / 20

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

(24x) - (49((149 - 17x) / 20)) = 22

Multiply both sides by 20 to eliminate the fraction:

480x - 14949 + 935x = 440

Combine like terms:

1415x = 14989

Divide both sides by 1415:

x = 14989 / 1415

x = 10.6

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

v = (149 - 17(10.6)) / 20

v = (149 - 180.2) / 20

v = (-31.2) / 20

v = -1.56

### Answer: v = -1.56, x = 10.6

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of g's in both equations are the same:

1) Multiply the first equation by 91:
357t + 371g = 13257
2) Multiply the second equation by 41:
386t - 3731g = 1732

Now, subtract the first equation from the second equation to eliminate the g term:

(386t - 357t) - (371g - 371g) = 1732 - 13257
29t = -11525

Now, divide by 29:
t = -11525/29
t = -398

Now that we have the value of t, substitute it into one of the original equations to find the value of g. We'll use the first equation:

39t + 41g = 147
39(-398) + 41g = 147
-15342 + 41g = 147

Add 15342 to both sides:
41g = 15342 + 147
41g = 15589

Divide by 41:
g = 15589/41
g = 380

### Answer: t = -398, g = 380

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.

Llama 3 8B:

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

First, we can solve the second equation for c:

c = (48o + 36) / 55

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

6((48o + 36) / 55) + 55o = 112

Multiply both sides by 55 to eliminate the fraction:

108o + 216 + 330o = 6160

Combine like terms:

438o = 5944

Divide both sides by 438:

o = 5944 / 438

o = 13.5

Now that we have found o, we can substitute this value back into one of the original equations to find c. We'll use the second equation:

55c - 48(13.5) = 36

55c - 648 = 36

Add 648 to both sides:

55c = 684

Divide both sides by 55:

c = 684 / 55

c = 12.4

So, the values of c and o that satisfy the system of equations are:

c = 12.4
o = 13.5

### Answer: c = 12.4, o = 13.5

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.

Llama 3 8B:

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

First, we can solve the first equation for w:

8w = 170 - 68u
w = (170 - 68u) / 8

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

71((170 - 68u) / 8) - 94u = 8

Multiply both sides by 8 to eliminate the fraction:

71(170 - 68u) - 94u*8 = 8*8

Expand and simplify:

12170 - 4802u - 752u = 64

Combine like terms:

12170 - 5254u = 64

Add 5254u to both sides:

12170 = 64 + 5254u

Subtract 64 from both sides:

12106 = 5254u

Divide both sides by 5254:

u = 12106 / 5254
u = 2.3

Now that we have found u, we can substitute this value back into one of the original equations to find w. We'll use the first equation:

8w + 68u = 170
8w + 68(2.3) = 170

Multiply 68 by 2.3:

8w + 156.4 = 170

Subtract 156.4 from both sides:

8w = 13.6

Divide both sides by 8:

w = 13.6 / 8
w = 1.7

So, the values of u and w that satisfy the system of equations are:

u = 2.3
w = 1.7

### Answer: u = 2.3, w = 1.7

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

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of r's in both equations are the same:

1) Multiply the first equation by 38:
256*r + 304*f = 3508

2) Multiply the second equation by 8:
776*f + 304*r = 1456

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

776*f - 256*r = 1456 - 3508
776*f - 256*r = -3262

Now, add 256*r to both sides:

776*f = -3262 + 256*r

Now, divide both sides by 776:

f = (-3262 + 256*r) / 776

Now, substitute this expression for f into one of the original equations, say the first equation:

68*r + 8*(-3262 + 256*r) = 92

Expand and simplify:

68*r - 26016 + 2048*r = 92

Combine like terms:

2116*r - 26016 = 92

Add 26016 to both sides:

2116*r = 26008

Divide both sides by 2116:

r = 26008 / 2116

r = 12.25

Now that we have the value of r, we can find the value of f by substituting r into the expression we found earlier:

f = (-3262 + 256*12.25) / 776

f = (-3262 + 3130) / 776

f = 868 / 776

f = 1.12

### Answer: r = 12.25, f = 1.12

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).

Llama 3 8B:

Let's solve the system of equations.

From the first equation, we have:

67d - 37r = 50

From the second equation, we have:

39r - 21d = 16

We can multiply the first equation by 21 and the second equation by 37 to make the coefficients of d equal:

1437d - 1357r = 1070
1439r - 777d = 592

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

-78d = 478

Dividing both sides by -78, we get:

d = -478/78
d = -6.23

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

67d - 37r = 50
67(-6.23) - 37r = 50
-416.01 - 37r = 50

Adding 416.01 to both sides:

-37r = 466.01

Dividing both sides by -37:

r = 466.01/37
r = 12.59

### Answer: d = -6.23, r = 12.59

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.

Llama 3 8B:

Let's solve the system of simultaneous linear equations.

First equation: 163 = 50x + a

Second equation: 24 = 98x - 84a

We can solve this system by substituting the expression for a from the first equation into the second equation.

Substitute a = 163 - 50x into the second equation:

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

Expand and simplify:

24 = 98x - 13692 + 4200x
24 = 4588x - 13692

Add 13692 to both sides:

13616 = 4588x

Divide both sides by 4588:

x = 13616/4588
x = 3

Now that we have found x, we can find a by substituting x into the first equation:

163 = 50(3) + a
163 = 150 + a

Subtract 150 from both sides:

13 = a

So, the values of x and a are:

x = 3
a = 13

### Answer: x = 3, a = 13

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.

Llama 3 8B:

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

First, we can multiply both sides of the first equation by 44 to get:

2952p + 792b = 4840

Now, we can multiply both sides of the second equation by 67 to get:

5494b - 2952p = 3866

Now, we can add both equations to eliminate the p variable:

5494b + 792b = 4840 + 3866
6286b = 8716

Now, we can divide both sides by 6286 to solve for b:

b = 8716/6286
b = 1.4

Now that we have the value of b, we can substitute it into one of the original equations to solve for p. We'll use the first equation:

67p + 18(1.4) = 110

67p + 25.2 = 110

Subtract 25.2 from both sides:

67p = 84.8

Divide both sides by 67:

p = 84.8/67
p = 1.26

So, the values of p and b are:

p = 1.26
b = 1.4

### Answer: p = 1.26, b = 1.4

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.

Llama 3 8B:

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

The first equation is:

63c - 36e = 27

The second equation is:

8c + 32e = 69

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

First, we can multiply the two equations by necessary multiples such that the coefficients of e's in both equations are the same:

1) Multiply the first equation by 4:

252c - 144e = 108

2) Multiply the second equation by 3:

24c + 96e = 207

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

(24c + 96e) - (252c - 144e) = 207 - 108
24c + 96e - 252c + 144e = 99
-228c = 99

Now, divide by -228:

c = -99/228
c = -27/76

Now that we have the value of c, we can substitute it into one of the original equations to find the value of e. We'll use the first equation:

63c - 36e = 27

Substitute c = -27/76:

63(-27/76) - 36e = 27

Simplify:

-1965/76 - 36e = 27

Multiply both sides by -76 to eliminate the fraction:

-1965 - 2736e = -76*27

Add 1965 to both sides:

-2736e = -1103

Divide by -2736:

e = 1103/2736
e = 1103/2736

### Answer: c = -27/76, e = 1103/2736.

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

Llama 3 8B:

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

First, we will multiply both equations by necessary multiples such that the coefficients of p's in both equations are the same:

1) Multiply the first equation by 51:
51 * 26 * x + 51 * 29 * p = 51 * 107

2) Multiply the second equation by 29:
29 * 61 * x - 29 * 51 * p = 29 * 4

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

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

Simplify the equation:

23 * x = 51 * 107 - 29 * 4

x = (51 * 107 - 29 * 4) / 23

x = 53

Now that we have the value of x, we can substitute it into one of the original equations to find the value of p. We will use the first equation:

26 * x + 29 * p = 107

26 * 53 + 29 * p = 107

1378 + 29 * p = 107

29 * p = -1271

p = -1271 / 29

p = -43.7

### Answer: x = 53, p = -43.7

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.

Llama 3 8B:

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

From the second equation, we can express g in terms of l:

g = (17 + 10l) / 31

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

((29 * l) + (17 * ((17 + 10l) / 31))) = 68

Simplify the equation:

((29 * l) + (17 * (17/31 + 10l/31))) = 68

Combine like terms:

((29 * l) + (17 * 17/31) + (17 * 10l/31)) = 68

Simplify further:

(29l + 17 + 10l) = 68

Combine like terms:

39l + 17 = 68

Subtract 17 from both sides:

39l = 51

Divide both sides by 39:

l = 51/39

l = 1.3077 (approximately)

Now that we have the value of l, we can find the value of g:

g = (17 + 10(1.3077)) / 31

g ≈ 2.3459

### Answer: g ≈ 2.3459, l ≈ 1.3077.

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.

Llama 3 8B:

We can solve this system of equations by multiplying the two equations by necessary multiples such that the coefficients of c's in both equations are the same.

First, multiply the first equation by 26 and the second equation by 54:

104*a - 702*c = 520
1312*a - 1428*c = 1581

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

1208*a = 1061

Now, divide by 1208:

a = 1061/1208

a = 0.88

Now that we have the value of a, substitute it into one of the original equations to find the value of c. We'll use the first equation:

33*a - 54*c = 20

33*(0.88) - 54*c = 20

33*0.88 - 54*c = 20

29.04 - 54*c = 20

Subtract 20 from both sides:

29.04 - 54*c - 20 = 0

-54*c = -9.04

Divide by -54:

c = 9.04/54

c = 0.17

### Answer: a = 0.88, c = 0.17

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of d's in both equations are the same:

1) Multiply the first equation by 84:
84(71d + 9j = 132) => 5884d + 756j = 11088

2) Multiply the second equation by 1:
43j - 84d = 91 => 43j - 84d = 91

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

(5884d + 756j = 11088) - (43j - 84d = 91)
5884d + 756j - 43j + 84d = 11088 - 91
5927d + 713j = 11097

Now, we can solve for j:

713j = 11097 - 5927d
j = (11097 - 5927d) / 713

Now that we have the expression for j, we can substitute it into one of the original equations to solve for d. Let's use the first equation:

71d + 9j = 132
71d + 9((11097 - 5927d) / 713) = 132

Now, we can simplify the equation:

71d + 9((11097 - 5927d) / 713) = 132
71d + 9((11097 - 5927d) / 713) = 132
71d + 9(11097 / 713 - 5927d / 713) = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132
71d + 99 - 5927d / 713 = 132

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.

Llama 3 8B:

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

First, we can solve the first equation for o:

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

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

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

Simplify the equation:

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

Multiply both sides by 81 to eliminate the fraction:

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

Expand and simplify:

7293n + 23(163 - 26n) = 11643

Distribute the 23:

7293n + 23(163) - 23(26n) = 11643

Combine like terms:

7293n + 3751 - 598n = 11643

Combine the terms with n:

5995n = 7902

Divide both sides by 5995:

n = 7902 / 5995

n = 1.32

Now that we have found n, we can substitute it back into one of the original equations to find o. We'll use the first equation:

(81 * o) + (26 * 1.32) = 163

(81 * o) + 34.32 = 163

Subtract 34.32 from both sides:

(81 * o) = 128.68

Divide both sides by 81:

o = 128.68 / 81

o = 1.59

So, the values of o and n are:

o = 1.59
n = 1.32

### Answer: o = 1.59, n = 1.32

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of w's in both equations are the same:

1) Multiply the first equation by 67:
67 * (46 * s - 61 * w) = 67 * 2
2) Multiply the second equation by 61:
61 * (61 * s + 67 * w) = 61 * 178

Now, we can simplify and rewrite the equations:

1) 67 * 46 * s - 67 * 61 * w = 134
2) 61 * 61 * s + 61 * 67 * w = 10938

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

(61 * 61 * s + 61 * 67 * w) - (67 * 46 * s - 67 * 61 * w) = 10938 - 134
61 * 61 * s + 61 * 67 * w - 67 * 46 * s + 67 * 61 * w = 10904

Combine like terms:

(61 * 61 - 67 * 46) * s = 10904
3721 * s = 10904

Now, divide by 3721:

s = 10904 / 3721
s = 2.93

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

46 * s - 61 * w = 2
46 * 2.93 - 61 * w = 2

Simplify:

135.78 - 61 * w = 2

Subtract 135.78 from both sides:

-61 * w = -133.78

Divide by -61:

w = 133.78 / 61
w = 2.20

So, the values of w and s are approximately 2.20 and 2.93, respectively.

### Answer: w ≈ 2.20, s ≈ 2.93.

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of i's in both equations are the same:

1) Multiply the first equation by 39:
195*k - 312*i = 3396
2) Multiply the second equation by 51:
1977*i + 408*k = 9843

Now, subtract the first equation from the second equation to eliminate the i term:

(1977*i - 195*k) + 408*k = 9843 - 3396
1977*i + 213*k = 6447

Now, we can solve for i:

i = (6447 - 213*k) / 1977

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

51*k - 8*((6447 - 213*k) / 1977) = 86

Simplify the equation:

51*k - 32.4 + 16.76*k = 86

Combine like terms:

67.76*k = 118.6

Divide by 67.76:

k = 1.75

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

i = (6447 - 213*1.75) / 1977
i = 6447 - 369.25
i = 6077.75 / 1977
i = 3.07

### Answer: i = 3.07, k = 1.75

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

Llama 3 8B:

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

First, we can solve the second equation for l:

l = 126 - 93m

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

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

Expand and simplify:

26m + 2106 - 1593m = 146

Combine like terms:

-1567m = -1960

Divide by -1567:

m = 1960/1567

m ≈ 1.25

Now that we have found m, we can find l by substituting m back into one of the original equations. We'll use the second equation:

l = 126 - 93(1.25)

l = 126 - 116.25

l ≈ 9.75

So, the values of l and m are approximately:

l ≈ 9.75
m ≈ 1.25

### Answer: l ≈ 9.75, m ≈ 1.25

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

Llama 3 8B:

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

We have two equations:

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

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

First, we can multiply equation (1) by 29 and equation (2) by 8 to make the coefficients of 'f' in both equations the same:

29(1) => 232f + 1131h = 1914
8(2) => 232f + 368h = 952

Now, subtract equation (2) from equation (1) to eliminate 'f':

(1914 - 952)h = 1914 - 952
962h = 962

Now, divide both sides by 962:

h = 1

Now that we have the value of 'h', we can substitute it into one of the original equations to find the value of 'f'. Let's use equation (1):

(8 * f) + (39 * 1) = 66
8f + 39 = 66

Subtract 39 from both sides:

8f = 27

Divide both sides by 8:

f = 27/8
f = 3.375

### Answer: h = 1, f = 3.375

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.

Llama 3 8B:

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

First, we can solve the first equation for k:

k = (109 - 22b) / 23

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

62((109 - 22b) / 23) - 69b = 14

Multiply both sides by 23 to eliminate the fraction:

1462 - 1032b - 1557b = 322

Combine like terms:

-2588b = -1140

Divide both sides by -2588:

b = 1140 / 2588

b ≈ 0.44

Now that we have found b, we can substitute it back into one of the original equations to find k. We'll use the first equation:

22b + 23k = 109

22(0.44) + 23k = 109

9.68 + 23k = 109

Subtract 9.68 from both sides:

23k = 99.32

Divide both sides by 23:

k = 99.32 / 23

k ≈ 4.31

So, the values of k and b that satisfy the system of equations are:

k ≈ 4.31
b ≈ 0.44

### Answer: k ≈ 4.31, b ≈ 0.44.

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.

Llama 3 8B:

Let's solve the system of linear equations step by step.

First, we can multiply equation (2) by 2 to make the coefficients of s in both equations the same:

2. 126m - 4s = 196

Now we can subtract equation (1) from equation (2) to eliminate the s variable:

(126m - 4s) - (84m - 55s) = 196 - 1
42m + 51s = 195

Next, we can multiply equation (1) by 63 to make the coefficients of m in both equations the same:

1. 5292m - 3465s = 63

Now we can subtract equation (1) from equation (2) to eliminate the m variable:

(126m - 4s) - (5292m - 3465s) = 196 - 63
-5166m + 3461s = 133

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

42m + 51s = 195
-5166m + 3461s = 133

We can solve this system using substitution or elimination. Let's use elimination. We can multiply equation (1) by 3461 and equation (2) by 51 to make the coefficients of s in both equations the same:

1. 145422m - 178355s = 67815
2. -26346m + 17531s = 8333

Now we can subtract equation (1) from equation (2) to eliminate the s variable:

(145422m - 178355s) - (-26346m + 17531s) = 67815 - 8333
171768m = 49582

Now we can solve for m:

m = 49582 / 171768
m = 0.288

Now that we have the value of m, we can substitute it into one of the original equations to solve for s. Let's use equation (1):

84m - 55s = 1
84(0.288) - 55s = 1
23.52 - 55s = 1

Now we can solve for s:

s = (1 - 23.52) / -55
s = -22.52 / -55
s = 0.408

### Answer: m = 0.288, s = 0.408

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.

Llama 3 8B:

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

From the first equation, we can express b in terms of k:

6b + 5k = 105
6b = 105 - 5k
b = (105 - 5k) / 6

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

95k - 51((105 - 5k) / 6) = 67

Multiply both sides by 6 to eliminate the fraction:

570k - 51(105 - 5k) = 402

Expand and simplify:

570k - 5335 + 255k = 402
825k - 5335 = 402

Add 5335 to both sides:

825k = 6037

Divide by 825:

k = 6037 / 825
k = 7.33

Now that we have found k, we can find b by substituting k back into one of the original equations. We'll use the first equation:

6b + 5k = 105
6b + 5(7.33) = 105

Multiply 5 by 7.33:

6b + 36.65 = 105

Subtract 36.65 from both sides:

6b = 68.35

Divide by 6:

b = 68.35 / 6
b = 11.39

### Answer: b = 11.39, k = 7.33

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of d's in both equations are the same:

1) Multiply the first equation by 40 and the second equation by 62:

1320d + 3860u = 4560
1984u + 2480d = 5118

2) Subtract the second equation from the first equation to eliminate d:

1320d - 1984u = 4560 - 5118
-1320d + 1984u = -5518

3) Simplify the equation:

-1320d + 1984u = -5518

4) Now, we can solve for u:

u = (-5518 + 1320d) / 1984

5) Substitute the expression of u into one of the original equations, say the first equation:

33d + 62(((-5518 + 1320d) / 1984)) = 114

6) Simplify the equation:

33d + 62((-5518 / 1984) + (1320d / 1984)) = 114

7) Simplify further:

33d - 5518/31 + 1320d/31 = 114

8) Combine like terms:

33d + 1320d/31 - 5518/31 = 114

9) Simplify:

(33 + 1320/31)d - 5518/31 = 114

10) Add 5518/31 to both sides:

(33 + 1320/31)d = 114 + 5518/31

11) Simplify:

(33 + 1320/31)d = 6326/31

12) Multiply both sides by 31:

(33 + 1320/31)d*31 = 6326/31*31

13) Simplify:

33d + 1320d = 6326

14) Combine like terms:

1353d = 6326

15) Divide both sides by 1353:

d = 6326/1353

16) Now that we have the value of d, substitute it into the expression of u:

u = (-5518 + 1320d) / 1984
u = (-5518 + 1320(6326/1353)) / 1984
u = (-5518 + 8328) / 1984
u = 2810 / 1984

17) Simplify:

u = 1.42

So, the values of d and u are:

d = 6326/1353 ≈ 4.65
u = 1.42

### Answer: d ≈ 4.65, u ≈ 1.42.

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

Llama 3 8B:

Let's solve the system of equations.

First, we can multiply the second equation by 5 to make the coefficients of p in both equations the same:

100c - 335p = 65

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

5c + 28p = 102
100c - 335p = 65

Adding the two equations, we get:

105c = 167

Now, we can solve for c:

c = 167/105
c = 1.57 (approximately)

Now that we have the value of c, we can substitute it into one of the original equations to solve for p. We'll use the first equation:

5c + 28p = 102

Substituting c = 1.57, we get:

5(1.57) + 28p = 102

Simplifying, we get:

7.85 + 28p = 102

Subtracting 7.85 from both sides, we get:

28p = 94.15

Dividing both sides by 28, we get:

p = 94.15/28
p = 3.36 (approximately)

### Answer: c ≈ 1.57, p ≈ 3.36

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.

Llama 3 8B:

Let's solve the system of linear equations.

We can start by multiplying the two equations by necessary multiples such that the coefficients of r's in both equations are the same:

1) Multiply the first equation by 76:
44r + 912q = 11208
2) Multiply the second equation by 58:
568q - 4484r = 4424

Now, add both equations to eliminate the r term:

(44r + 912q) + (568q - 4484r) = 11208 + 4424
912q + 568q = 11208 + 4424
1480q = 15632

Now, divide by 1480:

q = 15632/1480
q = 10.53

Now that we have the value of q, we can substitute it into one of the original equations to find the value of r. We'll use the first equation:

58r + 12q = 147
58r + 12(10.53) = 147
58r + 126.36 = 147

Subtract 126.36 from both sides:

58r = 20.64

Divide by 58:

r = 20.64/58
r = 0.357

### Answer: r = 0.357, q = 10.53

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.

Llama 3 8B:

Let's solve the system of simultaneous linear equations.

We have:

1) 47v - 3k = 10 ... (Equation 1)
2) 73v + 2k = 128 ... (Equation 2)

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

First, we'll multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of k in both equations the same:

1) 94v - 6k = 20 ... (Equation 1 multiplied by 2)
2) 219v + 6k = 384 ... (Equation 2 multiplied by 3)

Now, we'll subtract Equation 1 from Equation 2 to eliminate k:

(219v + 6k) - (94v - 6k) = 384 - 20
225v = 364

Now, we'll solve for v:

v = 364/225
v = 52/29
v = 1.793 (approximately)

Now that we have the value of v, we can substitute it into one of the original equations to find the value of k. We'll use Equation 1:

47v - 3k = 10
47(1.793) - 3k = 10
83.531 - 3k = 10

Now, we'll solve for k:

-3k = -73.531
k = 73.531/3
k = 24.510 (approximately)

So, the values of v and k are approximately 1.793 and 24.510, respectively.

### Answer: v ≈ 1.793, k ≈ 24.510.

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?

Llama 3 8B:

Let's solve the system of equations.

We have:

1) 89p - 41q = 60
2) 27p + 91q = 124

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

First, we can multiply equation (1) by 41 and equation (2) by 89 to make the coefficients of q in both equations the same:

1) 3647p - 1681q = 2460
2) 2397p + 8039q = 10976

Now, we can subtract equation (1) from equation (2) to eliminate q:

2397p + 8039q - 3647p + 1681q = 10976 - 2460
775p = 8426

Now, we can solve for p:

p = 8426/775
p = 10.9

Now that we have the value of p, we can substitute it into one of the original equations to solve for q. Let's use equation (1):

89p - 41q = 60
89(10.9) - 41q = 60
969.1 - 41q = 60

Now, we can solve for q:

-41q = -909.1
q = 909.1/41
q = 22.2

So, the values of p and q are:

p = 10.9
q = 22.2

### Answer: p = 10.9, q = 22.2

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

Llama 3 8B:

Let's solve the system of equations.

From the first equation, we can express u in terms of d:

u = (12 + 96d) / 88

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

(27((12 + 96d) / 88)) + (36d) = 71

Simplify the equation:

(27(12 + 96d) / 88) + 36d = 71

Multiply both sides by 88 to eliminate the fraction:

243 + 2592d + 3168d = 6232

Combine like terms:

4520d = 3989

Divide both sides by 4520:

d = 3989 / 4520

d = 0.882

Now that we have found d, we can find u:

u = (12 + 96(0.882)) / 88

u = (12 + 85.248) / 88

u = 97.248 / 88

u = 1.104

### Answer: u = 1.104, d = 0.882

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of f's in both equations are the same:

1) Multiply the first equation by 2:
40n - 36f = 18

2) Multiply the second equation by 18:
54n - 36f = 1260

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

(54n - 40n) - (36f - 36f) = 1260 - 18
14n = 1242

Now, divide by 14:

n = 1242/14
n = 89

Now that we have the value of n, substitute it into one of the original equations to find the value of f. We'll use the first equation:

20n - 18f = 9
20(89) - 18f = 9
1780 - 18f = 9

Subtract 1780 from both sides:

-18f = -1771
f = 1771/(-18)
f = -98.5

### Answer: f = -98.5, n = 89.

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.

Llama 3 8B:

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

First, we can solve the first equation for l:

l = (133 - 97j) / 7

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

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

Multiply both sides of the equation by 7 to eliminate the fraction:

154j + 37(133 - 97j) = 532

Expand and simplify the equation:

154j + 4933 - 3577j = 532

Combine like terms:

-2103j = -4401

Divide both sides by -2103:

j = 4401 / 2103

j = 2

Now that we have found j, we can find l by substituting j into one of the original equations. We'll use the first equation:

7l + 97(2) = 133

7l + 194 = 133

Subtract 194 from both sides:

7l = -61

Divide both sides by 7:

l = -61/7

l = -8.71 (rounded to two decimal places)

### Answer: j = 2, l = -8.71.

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of f's in both equations are the same:

1) Multiply the first equation by 84:
168d - 3884f = 4428
2) Multiply the second equation by 46:
368d + 3864f = 6118

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

(368d + 3864f) - (168d - 3884f) = 6118 - 4428
368d + 3864f - 168d + 3884f = 6118 - 4428
200d + 7748f = 1690

Now, divide both sides by 200:

d + 38.74f = 8.45

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

21d - 46f = 53
21(d + 38.74f) - 46f = 53
21(8.45) - 46f = 53
177.45 - 46f = 53

Now, subtract 53 from both sides:

177.45 - 46f - 53 = 0
-46f = -25.55

Now, divide both sides by -46:

f = 25.55/46
f = 0.55

Now that we have found f, we can substitute it back into the expression for d:

d + 38.74f = 8.45
d + 38.74(0.55) = 8.45
d + 21.29 = 8.45
d = 8.45 - 21.29
d = -12.84

### Answer: d = -12.84, f = 0.55

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of w's in both equations are the same:

1) Multiply the first equation by 68 and the second equation by 11:

476u + 748w = 7936
726u - 748w = 231

2) Now, add both equations to eliminate w:

1102u = 8167

3) Divide by 1102:

u = 8167/1102
u = 7.4

4) Now that we have the value of u, substitute it into one of the original equations to find the value of w. We'll use the first equation:

74u + 11w = 116
74(7.4) + 11w = 116
551 + 11w = 116

5) Subtract 551 from both sides:

11w = -435

6) Divide by 11:

w = -435/11
w = -39.5

So, the values of u and w that satisfy the system of equations are:

u = 7.4
w = -39.5

### Answer: u = 7.4, w = -39.5

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.

Llama 3 8B:

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

First, we can solve the first equation for f:

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

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

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

Multiply both sides by 76 to eliminate the fraction:

2827j + 2856 + 1272j = 10304

Combine like terms:

2549j = 7468

Divide both sides by 2549:

j = 7468 / 2549
j = 2.93 (approximately)

Now that we have found j, we can substitute it back into one of the original equations to find f. We'll use the first equation:

76f - 42(2.93) = 96

Simplify:

76f - 124.86 = 96

Add 124.86 to both sides:

76f = 220.86

Divide both sides by 76:

f = 220.86 / 76
f = 2.91 (approximately)

### Answer: f ≈ 2.91, j ≈ 2.93.

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.

Llama 3 8B:

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

First, we can solve the second equation for e:

e = (1 + 69u) / 63

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

68u + 32((1 + 69u) / 63) = 174

Multiply both sides by 63 to eliminate the fraction:

4256u + 2048 = 10872

Subtract 2048 from both sides:

4256u = 8824

Divide both sides by 4256:

u = 8824 / 4256

u = 2

Now that we have found u, we can find e by substituting u back into one of the original equations. We'll use the second equation:

e = (1 + 69(2)) / 63

e = (1 + 138) / 63

e = 139 / 63

e = 13/7

### Answer: u = 2, e = 13/7

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.

Llama 3 8B:

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

First, we will multiply the two equations by necessary multiples such that the coefficients of n's in both equations are the same:

1) Multiply the first equation by 39 and the second equation by 4:

195p + 156n = 5013
96p + 156n = 616

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

195p - 96p = 5013 - 616
99p = 4397

Now, divide by 99:

p = 4397/99
p = 44

Now that we have the value of p, substitute it in one of the original equations to find the value of n. We will use the first equation:

57p + 4n = 129
57(44) + 4n = 129
2512 + 4n = 129

Subtract 2512 from both sides:

4n = -2383
n = -2383/4
n = -599.25

### Answer: p = 44, n = -599.25

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.

Llama 3 8B:

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

First, we can solve the second equation for y:

60y + 14z = 116
60y = 116 - 14z
y = (116 - 14z) / 60

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

66z - 44((116 - 14z) / 60) = 32

Multiply both sides by 60 to eliminate the fraction:

3960z - 2640(116 - 14z) = 1920

Expand and simplify:

3960z - 307200 + 37120z = 1920
46780z = 308320

Divide both sides by 46780:

z = 308320 / 46780
z = 6.6

Now that we have found z, we can substitute it back into one of the original equations to find y. We'll use the second equation:

60y + 14(6.6) = 116

60y + 92.4 = 116

Subtract 92.4 from both sides:

60y = 23.6

Divide both sides by 60:

y = 23.6 / 60
y = 0.39

### Answer: y = 0.39, z = 6.6

Expected answer: {y: 901/572, z: 439/286}

Correct? No

Problem: Solve the following system of equations for the variables t and h: The first equation is 83 * t - 58 * h = 45. The second equation is 69 * h + 11 * t = 124.

Llama 3 8B:

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

First, we can multiply both sides of the first equation by 58 to get:

83t = 45 + 58h

Next, we can multiply both sides of the second equation by 11 to get:

769h + 121t = 1374

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

769h - 83t = 1374 - 45
= 1329

Now, we can divide both sides by 83 to get:

h = (1329 - 83t) / 769

Now, we can substitute this expression for h into one of the original equations. Let's use the first equation:

83t - 58((1329 - 83t) / 769) = 45

To simplify this equation, we can multiply both sides by 769 to get rid of the fraction:

61957 - 9764t = 34965

Next, we can subtract 34965 from both sides to get:

-26992 = -9764t

Finally, we can divide both sides by -9764 to solve for t:

t = 26992 / 9764
= 2.77

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

69h + 11(2.77) = 124

To solve for h, we can subtract 30.67 from both sides:

69h = 93.33

Finally, we can divide both sides by 69 to solve for h:

h = 93.33 / 69
= 1.35

### Answer: t = 2.77, h = 1.35

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?

Llama 3 8B:

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

First, we can solve the second equation for h:

h = (12 * o + 9) / 16

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

(79 * ((12 * o + 9) / 16)) - (61 * o) = 9

Simplify the equation:

(946.5 * o + 693) - 61 * o = 9

Combine like terms:

885.5 * o = -684

Divide both sides by 885.5:

o = -684 / 885.5

o ≈ -0.77

Now that we have the value of o, substitute it back into the expression for h:

h = (12 * (-0.77) + 9) / 16

h = (-9.24 + 9) / 16

h = 0.76 / 16

h ≈ 0.0475

So, the values of o and h are approximately o ≈ -0.77 and h ≈ 0.0475.

### Answer: o ≈ -0.77, h ≈ 0.0475.

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

Llama 3 8B:

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

First, we can solve the first equation for s:

s = (139 - 4y) / 56

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

65y - 90((139 - 4y) / 56) = 16

Multiply both sides by 56 to eliminate the fraction:

65y - 90(139 - 4y) = 16 * 56

Expand and simplify:

65y - 12570 + 360y = 896

Combine like terms:

425y = 12590

Divide by 425:

y = 12590 / 425

y = 29.5

Now that we have found y, substitute it back into one of the original equations to find s. We'll use the first equation:

4 * 29.5 + 56 * s = 139

Expand and simplify:

117 + 56s = 139

Subtract 117 from both sides:

56s = 22

Divide by 56:

s = 22 / 56

s = 0.4

### Answer: s = 0.4, y = 29.5

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of z's in both equations are the same:

1) Multiply the first equation by 45:
1825d - 180z = 3375
2) Multiply the second equation by 4:
160d + 180z = 648

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

(160d + 180z) - (1825d - 180z) = 648 - 3375
160d - 1825d = 648 - 3375
-1665d = -2727
d = 2727/1665
d = 1.64

Now that we have the value of d, we can substitute it into one of the original equations to find the value of z. We'll use the first equation:

42d - 4z = 75
42(1.64) - 4z = 75
67.68 - 4z = 75
-4z = 75 - 67.68
-4z = 7.32
z = -7.32/4
z = -1.83

### Answer: d = 1.64, z = -1.83

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.

Llama 3 8B:

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

First, we can solve the second equation for 'a':

(42 * a) + (6 * o) = 75
42 * a = 75 - 6 * o
a = (75 - 6 * o) / 42

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

(42 * o) + (24 * ((75 - 6 * o) / 42)) = 142

Simplify the equation:

42 * o + 24 * ((75 - 6 * o) / 42) = 142
42 * o + 24 * (75 / 42 - 6 * o / 42) = 142
42 * o + 24 * (75 / 42) - 24 * 6 * o / 42 = 142
42 * o + 18 - 24 * 6 * o / 42 = 142
42 * o + 18 - 12 * o = 142
30 * o + 18 = 142
30 * o = 142 - 18
30 * o = 124
o = 124 / 30
o = 4

Now that we have the value of 'o', we can substitute it back into one of the original equations to find the value of 'a'. We'll use the second equation:

(42 * a) + (6 * 4) = 75
42 * a + 24 = 75
42 * a = 75 - 24
42 * a = 51
a = 51 / 42
a = 1.21

So, the values of 'a' and 'o' are approximately 1.21 and 4, respectively.

### Answer: a ≈ 1.21, o ≈ 4.

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of r's in both equations are the same:

1) Multiply the first equation by 16 and the second equation by 2:

624*r - 32*p = 720 and 32*p - 168*r = 72

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

624*r - 32*p - (32*p - 168*r) = 720 - 72

This simplifies to:

792*r = 648

Now, divide both sides by 792:

r = 648/792

r = 3/4

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

39*(3/4) - 2*p = 45

Simplify the left-hand side:

29.25 - 2*p = 45

Subtract 29.25 from both sides:

-2*p = 15.75

Divide both sides by -2:

p = -15.75/2

p = -7.875

### Answer: p = -7.875, r = 3/4.

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

Llama 3 8B:

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

From equation (1), we can express 'd' in terms of 'w':

d = (7 + 52w) / 23

Now, substitute this expression for 'd' into equation (2):

(64w) - (8 * ((7 + 52w) / 23)) = 58

Simplify the equation:

64w - (56/23) - (416w/23) = 58

Combine like terms:

(48w - 56/23) = 58

Multiply both sides by 23 to eliminate the fraction:

1080w - 56 = 1318

Add 56 to both sides:

1080w = 1374

Divide both sides by 1080:

w = 1374/1080

w = 1.275

Now that we have the value of 'w', we can find the value of 'd':

d = (7 + 52(1.275)) / 23

d = (7 + 65.5) / 23

d = 72.5 / 23

d = 3.15

### Answer: d = 3.15, w = 1.275

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.

Llama 3 8B:

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

First, we can multiply the two equations by necessary multiples such that the coefficients of n's in both equations are the same:

1) Multiply the first equation by 47:
47(71z + 60n) = 47(184)
2) Multiply the second equation by 60:
60(52z - 47n) = 60(19)

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

47(71z + 60n) - 60(52z - 47n) = 47(184) - 60(19)
47(71z + 60n) - 60(52z - 47n) = 862 - 1140
47(71z + 60n) - 60(52z - 47n) = -278

Now, simplify the equation:

47(71z) + 47(60n) - 60(52z) + 60(47n) = -278
47(71z) - 60(52z) + 47(60n) + 60(47n) = -278
7z - 60z + 2820 + 2820 = -278
-53z + 5640 = -278

Now, add 278 to both sides:

-53z + 5640 = 0
-53z = -5640

Now, divide both sides by -53:

z = 5640/53
z = 106

Now that we have the value of z, we can substitute it into one of the original equations to find the value of n. We'll use the first equation:

71z + 60n = 184
71(106) + 60n = 184
7540 + 60n = 184

Now, subtract 7540 from both sides:

60n = -7356
n = -7356/60
n = -123

### Answer: n = -123, z = 106.

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

Llama 3 8B:

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

First, let's multiply both equations by necessary multiples such that the coefficients of e's in both equations are the same:

1) Multiply the first equation by 84:
588e + 756z = 1584
2) Multiply the second equation by 70:
693z - 588e = 1400

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

693z - 588e - (588e + 756z) = 1400 - 1584
693z - 588e - 588e - 756z = -84
-1053e = -84

Now, divide both sides by -1053:

e = 84/1053
e = 8/103

Now that we have the value of e, substitute it into one of the original equations to find the value of z. We'll use the first equation:

70e + 90z = 189
70(8/103) + 90z = 189

Multiply both sides by 103:

560 + 90z = 19383
90z = 19323
z = 19323/90
z = 214

### Answer: e = 8/103, z = 214

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.

Llama 3 8B:

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

From equation (1), we can express o in terms of f:

o = (95 + 44f) / 26

Now, substitute this expression for o into equation (2):

87f + 11((95 + 44f) / 26) = 169

Multiply both sides by 26 to eliminate the fraction:

2197f + 1215 + 121f = 4366

Combine like terms:

2318f + 1215 = 4366

Subtract 1215 from both sides:

2318f = 3151

Divide both sides by 2318:

f = 3151 / 2318

f = 1.36 (approximately)

Now that we have found f, we can find o by substituting f back into the expression we found earlier:

o = (95 + 44(1.36)) / 26

o = (95 + 59.84) / 26

o = 154.84 / 26

o = 5.96 (approximately)

### Answer: o ≈ 5.96, f ≈ 1.36.

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.

Llama 3 8B:

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

First, we can solve the first equation for z:

40*z - 20*p = 51
40*z = 51 + 20*p
z = (51 + 20*p) / 40

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

6*(51 + 20*p) / 40 + 58*p = 165

Multiply both sides by 40 to eliminate the fraction:

6*(51 + 20*p) + 58*p*40 = 165*40

Expand and simplify:

306 + 120*p + 2320*p = 6600

Combine like terms:

2446*p = 6294

Divide by 2446:

p = 6294 / 2446
p = 2.57 (approximately)

Now that we have found p, we can substitute it back into one of the original equations to find z. We'll use the first equation:

40*z - 20*p = 51
40*z - 20*2.57 = 51

Add 102.8 to both sides:

40*z = 153.8

Divide by 40:

z = 153.8 / 40
z = 3.845 (approximately)

### Answer: z ≈ 3.845, p ≈ 2.57.

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.

Llama 3 8B:

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

First, we can solve the second equation for f:

3f + 10s = 93
3f = 93 - 10s
f = (93 - 10s) / 3

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

(71s) - (89((93 - 10s) / 3)) = 5

Multiply both sides by 3 to eliminate the fraction:

213s - 267(93 - 10s) = 15

Expand and simplify:

213s - 24837 + 2670s = 15

Combine like terms:

1483s = 24952

Divide both sides by 1483:

s = 24952 / 1483
s = 16.8

Now that we have the value of s, we can find the value of f:

f = (93 - 10(16.8)) / 3
f = (93 - 168) / 3
f = -75 / 3
f = -25

### Answer: s = 16.8, f = -25

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

Correct? No