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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

40s - 91q = 37

Now, divide both sides by 40 to get:

s - 2q = 37/40

Now, add 2q to both sides to get:

s = 37/40 + 2q

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

30(37/40 + 2q) + 12q = 121

Expand and simplify:

111q + 37 = 121

Subtract 37 from both sides:

111q = 84

Divide both sides by 111:

q = 84/111

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

s = 37/40 + 2(84/111)

Simplify:

s = 37/40 + 16/111

Therefore, the values of q and s are 84/111 and 37/40 + 16/111, respectively.

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

Correct? No

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for b:

4 * b + 44 * m = 180

Subtracting 44m from both sides gives us:

4b = 180 - 44m

Dividing both sides by 4 gives us:

b = (180 - 44m) / 4

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

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

Expanding the right-hand side gives us:

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

Simplifying and rearranging gives us:

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

Expanding the right-hand side gives us:

79m - 6(180) + 6(44m) = 192

Simplifying and rearranging gives us:

79m - 1080 + 264m = 192

Subtracting 1080 from both sides gives us:

185m = 832

Dividing both sides by 185 gives us:

m = 4

Now that we have found m, we can substitute it into the expression for b that we found earlier:

b = (180 - 44m) / 4

Substituting m = 4 gives us:

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

Simplifying gives us:

b = (180 - 176) / 4

Simplifying further gives us:

b = 4

Therefore, the values of b and m are 4 and 4, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for o:

o = (28 + 15g) / 42

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

47(28 + 15g) / 42 + 29g = 141

Expand and simplify:

136 + 7g = 141

Subtract 136 from both sides:

7g = 5

Divide both sides by 7:

g = 5/7

Now that we have found g, we can find o:

o = (28 + 15(5/7)) / 42

o = (28 + 7.5) / 42

o = 35.5 / 42

o = 17/21

Therefore, the values of o and g are 17/21 and 5/7, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

12v - 6o = 21

From the second equation, we have:

76v - 45o = 50

Now, we can solve for v and o.

First, we can solve the first equation for v:

v = (21 + 6o) / 12

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

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

Expand and simplify:

140 + 76o - 45o = 50

166 - 31o = 50

31o = 116

o = 116 / 31

o = 3.71

Now that we have found o, we can find v:

v = (21 + 6(3.71)) / 12

v = (21 + 22.22) / 12

v = 43.22 / 12

v = 3.66

Therefore, the values of v and o are 3.66 and 3.71, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for f:

f = (138 - 25g) / 75

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

(138 - 25g) / 75 + 90g = 143

Now, simplify and solve for g:

138 - 25g + 90g = 143

g = 138 - 25g

g = 138 / 25

g = 5.52

Now, substitute this value for g into the first equation to find f:

f = (138 - 25g) / 75

f = (138 - 25(5.52)) / 75

f = 138 / 75

f = 1.84

Therefore, f = 1.84 and g = 5.52.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for y:

194 = 4y + 14n

Subtract 14n from both sides:

180 = 4y

Divide both sides by 4:

45 = y

Now, substitute y = 45 into the second equation:

7 = 65n - 79y

Substitute y = 45:

7 = 65n - 79(45)

Simplify:

7 = 65n - 3495

Add 3495 to both sides:

3502 = 65n

Divide both sides by 65:

53.15 = n

So, n = 53.15.

Now, substitute n = 53.15 into the first equation:

194 = 4y + 14n

Substitute n = 53.15:

194 = 4y + 14(53.15)

Simplify:

194 = 4y + 739

Subtract 739 from both sides:

120 = 4y

Divide both sides by 4:

30 = y

So, y = 30.

Therefore, the solution to the system of equations is y = 30 and n = 53.15.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for g:

g = (146 - 26l) / 28

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

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

Now simplify and solve for l:

6 = 41l - 53(146 - 26l) / 28
6 = 41l - 53(146) / 28 + 53(26l) / 28
6 = 41l - 146(53) / 28 + 53(26l) / 28
6 = 41l - 3998 + 146(26l) / 28
6 = 41l - 3998 + 692l
6 = 41l - 3306

Now, solve for l:

l = 6 / 41
l = 146 / 28
l = 5

Now that we have found l, we can substitute it into the first equation to find g:

g = (146 - 26l) / 28
g = (146 - 26(5)) / 28
g = (146 - 130) / 28
g = 16 / 28
g = 1 / 2

Therefore, the values of l and g that satisfy the two equations are l = 5 and g = 1/2.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for p:

p = 90 / 20 = 4.5

Now, substitute this value of p into the second equation:

89 * 4.5 + 7 * y = 98

Now, solve for y:

y = (98 - 89 * 4.5) / 7 = 11 / 7

So, the values of p and y are 4.5 and 11/7, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for k:

k = (17 + 22d) / 72

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

6d + 69(17 + 22d) / 72 = 96

Expand and simplify:

6d + 1258 / 72 = 96

Multiply both sides by 72:

432d + 1258 = 6720

Subtract 1258 from both sides:

432d = 5462

Divide both sides by 432:

d = 12

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

k = (17 + 22d) / 72
= (17 + 22(12)) / 72
= 17 / 72 + 22 / 72
= 1 / 4 + 2 / 7
= 3 / 7

Therefore, the values of k and d are 3/7 and 12, respectively.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for d:

d = (48 - 73h) / 33

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

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

Expand and simplify:

480 - 730h + 10h = 910

-730h + 10h = 430

-720h = 330

h = 330 / 720

h = 1/2

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

d = (48 - 73(1/2)) / 33

d = (48 - 36.5) / 33

d = 11.5 / 33

d = 1/3

Therefore, the values of d and h are 1/3 and 1/2, respectively.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

43q - 44e = 29

Multiplying both sides by -1, we get:

44e - 43q = -29

Now, adding the second equation to both sides of the above equation, we get:

30q + 43e = 130 + (-29)

Simplifying, we get:

30q + 43e = 101

Now, we have a linear equation in q and e. Solving for q, we get:

q = (101 - 43e) / 30

Now, substituting this value of q in the first equation, we get:

43(101 - 43e) / 30 - 44e = 29

Simplifying, we get:

123 - 129e = 29

Adding 129e to both sides, we get:

123 = 29 + 129e

Subtracting 29 from both sides, we get:

94 = 129e

Dividing both sides by 129, we get:

e = 94 / 129

Therefore, the value of e is 94/129.

Now, substituting this value of e in the equation q = (101 - 43e) / 30, we get:

q = (101 - 43(94/129)) / 30

Simplifying, we get:

q = 101 / 30 - (43/129)

Therefore, the value of q is 3 + (43/129).

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))

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for r:

r = 53 / (89 - 74a)

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

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

Now, simplify the right-hand side of the equation:

109 = 37a + 6(53 / (89 - 74a))
109 = 37a + 6(53 / 15)
109 = 37a + 6(3)
109 = 37a + 18

Now, solve for a:

a = 109 / 37
a = 3

Now that we have found a, we can substitute it into the first equation to find r:

r = 53 / (89 - 74a)
r = 53 / (89 - 74(3))
r = 53 / 15
r = 3

Therefore, the values of r and a are 3 and 3, respectively.

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.

CodeLlama 34B:

  To solve for 'g' and 'q', we need to use the two equations given.

From the first equation, we can write:

42g + 12q = 169

From the second equation, we can write:

12q - 50g = 19

Now, we can solve for 'g' and 'q' by adding the two equations:

42g + 12q = 169
12q - 50g = 19

Adding the two equations, we get:

54g + 12q = 188

Now, we can solve for 'g' by subtracting 12q from both sides:

54g = 188 - 12q

Substituting the value of 12q from the first equation, we get:

54g = 188 - 12(42)
54g = 188 - 492
54g = -324

Dividing both sides by 54, we get:

g = -6.3

Now, we can find 'q' by substituting the value of 'g' in the first equation:

42(-6.3) + 12q = 169
-260.4 + 12q = 169
12q = 439.4
q = 36.6

Therefore, the values of 'g' and 'q' are -6.3 and 36.6, respectively.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for s:

s = (54 + 11v) / 37

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

82 * (54 + 11v) / 37 - 62v = 41

Expand and simplify:

294 + 11v - 62v = 41

11v - 21 = 41

11v = 62

v = 5

Now that we have found v, we can substitute it into the first equation to find s:

s = (54 + 11v) / 37
= (54 + 11(5)) / 37
= 65 / 37

Therefore, s = 65/37 and v = 5.

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

Correct? No

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for c:

41c + 65z = 151
c = (151 - 65z) / 41

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

78z - 48(151 - 65z) / 41 = 48
78z - 48(151) / 41 + 48(65z) / 41 = 48
78z - 3968 / 41 + 296z / 41 = 48
78z - 3672 / 41 = 48
78z = 4336 / 41
z = 61

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

c = (151 - 65z) / 41
c = (151 - 65(61)) / 41
c = (151 - 3965) / 41
c = -3814 / 41
c = -93

Therefore, the values of c and z are -93 and 61, respectively.

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?

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for c:

c = 7/60

Now, substitute this value of c into the second equation:

7i + 76(7/60) = 148

Simplify:

7i + 49 = 148

Subtract 7i from both sides:

49 = 148 - 7i

Subtract 49 from both sides:

148 - 7i - 49 = 0

Add 7i to both sides:

7i = 99

Divide both sides by 7:

i = 14

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

c = 7/60

Therefore, the values of c and i are 7/60 and 14, respectively.

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

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

71v - 37e = 69

Now, from the second equation, we have:

41e + 76v = 184

We can solve for e in the first equation:

e = (69 + 37v) / 71

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

41((69 + 37v) / 71) + 76v = 184

Expand and simplify:

297 + 259v = 184

Subtract 297 from both sides:

259v = 87

Now, divide both sides by 259:

v = 87 / 259

Now, we can find e by substituting v into the first equation:

e = (69 + 37(87 / 259)) / 71

Simplify:

e = 11 / 259

Therefore, the values of e and v that satisfy the two equations are e = 11/259 and v = 87/259.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

25v + 69d = 113

From the second equation, we have:

26d + 42v = 85

Now, we can solve for 'v' in the first equation:

v = (113 - 69d) / 25

Now, substitute this expression for 'v' in the second equation:

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

Now, simplify and solve for 'd':

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

26d + 42(4) - 42(69d/25) = 85

26d + 168 - 287d = 85

-263d = -83

d = 3

Now that we have found 'd', we can find 'v':

v = (113 - 69d) / 25
= (113 - 69(3)) / 25
= (113 - 207) / 25
= -94 / 25
= -3

So, the values of 'd' and 'v' are 3 and -3, respectively.

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

Correct? No

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

CodeLlama 34B:

  To solve for g and z, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for g:

g = (33 + 91z) / 43

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

72(33 + 91z) / 43 - 3z = 68

Expand and simplify:

2197 + 643z - 3z = 68

Combine like terms:

1554 - 3z = 68

Add 3z to both sides:

1554 = 68 + 3z

Subtract 68 from both sides:

1486 = 3z

Divide both sides by 3:

495 = z

Now, substitute this value of z into the first equation to solve for g:

g = (33 + 91z) / 43
g = (33 + 91(495)) / 43
g = (33 + 4435) / 43
g = 4768 / 43
g = 111

Therefore, g = 111 and z = 495.

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.

CodeLlama 34B:

  To solve this system of equations, we can first solve the first equation for c:

50c + 12f = 92
50c = 92 - 12f
50c = 80 + 12f
c = 80/50 + 12/50f
c = 1.6 + 2.4f

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

36(1.6 + 2.4f) - 21f = 34
57.6 + 64.8f - 21f = 34
92.4f - 21f = 34
71.4f = 68
f = 68/71.4
f = 0.96

Now we can find c:

c = 1.6 + 2.4f
c = 1.6 + 2.4(0.96)
c = 1.6 + 2.288
c = 3.888

So, the quantity of cherries is approximately 3.888 and the quantity of figs is approximately 0.96.

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

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we can solve for u:

u = (7 + 75d) / 87

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

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

Now simplify and solve for d:

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

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

85d - 56 / 87 - 6175d / 87 = 54

85d - 623 / 87 = 54

85d = 623 / 87 + 54

85d = 116 / 87

d = 116 / 87 / 85

d = 1 / 87

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

u = (7 + 75d) / 87

u = (7 + 75(1/87)) / 87

u = (7 + 75/87) / 87

u = 7/87 + 75/87^2

u = 78/87^2

Therefore, the values of u and d are u = 78/87^2 and d = 1/87.

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?

CodeLlama 34B:

  Yes, I can help Bill solve the system of equations.

First, let's rewrite the first equation as:

75a - 4i = 42

We can solve for a by adding 4i to both sides:

75a = 42 + 4i

Now, let's rewrite the second equation as:

10i + 13a = 160

We can solve for i by subtracting 13a from both sides:

10i = 160 - 13a

Now we have two equations and two unknowns. We can substitute the expression for 10i from the second equation into the first equation:

75a = 42 + 4(160 - 13a)

Now we can simplify and solve for a:

75a = 42 + 640 - 52a

Subtracting 640 from both sides gives us:

17a = 42 + 52a

Subtracting 52a from both sides gives us:

12a = 42

Dividing both sides by 12 gives us:

a = 3

Now we can substitute a = 3 into either of the original equations to solve for i:

10i + 13(3) = 160

Subtracting 39 from both sides gives us:

6i = 121

Dividing both sides by 6 gives us:

i = 20

Therefore, the values of i and a are i = 20 and a = 3.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the second equation for c:

c = (13 + 18p) / 27

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

37p + 74(13 + 18p) / 27 = 183

Expand and simplify:

37p + 13(18p) / 27 = 183

Combine like terms:

51p = 183

Divide by 51:

p = 183 / 51

p = 3

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

c = (13 + 18p) / 27

c = (13 + 18(3)) / 27

c = 13 + 54 / 27

c = 13 + 2

c = 15

Therefore, the values of p and c are 3 and 15, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for k:

k = 37 / (48 - 30p)

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

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

Now simplify and solve for p:

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

16p + 33(37 / 18) = 105

16p + 33(2) = 105

16p + 66 = 105

16p = 39

p = 2.44

Now that we have p, we can find k:

k = 37 / (48 - 30p)

k = 37 / (48 - 30(2.44))

k = 37 / 14.56

k = 2.6

So, k = 2.6 and p = 2.44.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for v:

v = (14 + 69f) / 75

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

46f + 53((14 + 69f) / 75) = 110

Expand and simplify:

46f + 53(14/75) + 53f = 110

Combine like terms:

46f + 53f = 110 - 53(14/75)

Simplify:

99f = 110 - 53(14/75)

Solve for f:

f = (110 - 53(14/75)) / 99

Now, substitute this expression for f into the first equation to solve for v:

v = (14 + 69f) / 75

v = (14 + 69((110 - 53(14/75)) / 99)) / 75

Simplify:

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99)) / 75

v = (14 + 69(110/99) - 69(14/99

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for o:

o = (131 - 13g) / 7

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

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

Expand and simplify:

89g - 1039 + 91g = 37

Combine like terms:

190g - 1039 = 37

Add 1039 to both sides:

190g = 1116

Divide by 190:

g = 6

Now that we have found g, we can find o:

o = (131 - 13g) / 7
= (131 - 13(6)) / 7
= (131 - 78) / 7
= 53 / 7
= 7

So, the values of o and g are 7 and 6, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for d:

d = (38 + 60k) / 88

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

33k - 11(38 + 60k) / 88 = 46

Expand and simplify:

33k - 38 - 11(60k) / 88 = 46

Combine like terms:

22k - 38 = 46

Add 38 to both sides:

22k = 84

Divide by 22:

k = 4

Now that we have found k, we can substitute it into the first equation to find d:

d = (38 + 60k) / 88
= (38 + 60(4)) / 88
= 168 / 88
= 19 / 7

Therefore, the values of d and k are d = 19/7 and k = 4.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for z:

24z + 72y = 139

z = (139 - 72y) / 24

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

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

Expand and simplify:

26 - 168y / 24 + 82y = 96

Combine like terms:

-106y / 24 = -32

y = 32 / 106

Now, substitute this value of y into one of the original equations to find z:

24z + 72(32 / 106) = 139

z = (139 - 24(32 / 106)) / 72

z = 24 / 72

z = 1 / 3

So, y = 32 / 106 and z = 1 / 3.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for v:

v = (1 + 29o) / 87

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

(8 * (1 + 29o) / 87) + (30 * o) = 91

Expand and simplify:

(8 / 87) + (29 / 87)o = 91 / 87

o = 91 / 87 - 8 / 87

o = 11 / 87

Now that we have found o, we can find v:

v = (1 + 29(11 / 87)) / 87

v = (1 + 319 / 87) / 87

v = 88 / 87

Therefore, the solution to the system of equations is v = 88/87 and o = 11/87.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for h:

h = (58 + 46p) / 23

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

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

Expand and simplify:

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

Combine like terms:

11p + 58 + 103p = 124

Subtract 58:

11p + 103p = 66

Subtract 103p:

11p = 66 - 103p

Subtract 11p:

-103p = 66 - 11p

Multiply by -1:

103p = 11p - 66

Add 11p:

114p = 66

Divide by 114:

p = 66 / 114

Now, substitute this expression for p into the first equation to solve for h:

h = (58 + 46(66 / 114)) / 23

Simplify:

h = (58 + 2976 / 114) / 23

Simplify:

h = 2976 / 257

Simplify:

h = 11

Therefore, h = 11 and p = 66 / 114.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for d:
19d = 120 - 6f
d = (120 - 6f) / 19

Now, substitute this expression for d into the second equation:
90((120 - 6f) / 19) - 42f = 69

Expand and simplify:
1140 - 576f - 42f = 69

Add 576f to both sides:
1140 - 42f = 69 + 576f

Subtract 42f from both sides:
1100 = 69 + 534f

Subtract 69 from both sides:
1031 = 534f

Divide both sides by 534:
f = 1031 / 534
f = 1.94

Now that we have found f, we can find d:
d = (120 - 6f) / 19
d = (120 - 6(1.94)) / 19
d = (120 - 11.64) / 19
d = 7.36 / 19
d = 0.38

Therefore, the values of d and f are 0.38 and 1.94, respectively.

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'?

CodeLlama 34B:

  Yes, I can solve this system of linear equations.

First, we can solve the first equation for 'r':

r = (127 - 42m) / 55

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

66m - 52(127 - 42m) / 55 = 44

Simplifying this expression, we get:

66m - 127m + 2594 / 55 = 44

Combine like terms:

-61m + 2594 / 55 = 44

Now, we can solve for 'm':

m = (2594 / 55 - 44) / -61

m = 11 / 3

Now that we have found 'm', we can find 'r' by substituting this value into the first equation:

r = (127 - 42(11/3)) / 55

r = 23 / 11

Therefore, the values of 'r' and 'm' are 23/11 and 11/3, respectively.

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

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for n:

n = (120 - 64w) / 31

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

57w + 71((120 - 64w) / 31) = 173

Expand and simplify:

57w + 71(120/31 - 64w/31) = 173

57w + 71(3 - 2w) = 173

114w + 147 = 173

Subtract 147 from both sides:

114w = 26

Divide both sides by 114:

w = 26/114

Now, substitute this value of w into one of the original equations to solve for n:

n = (120 - 64w) / 31

Substitute w = 26/114:

n = (120 - 64(26/114)) / 31

Expand and simplify:

n = (120 - 16/7) / 31

n = 31 - 16/7

n = 31 - 2

n = 29

Therefore, the values of n and w that satisfy the system of linear equations are n = 29 and w = 26/114.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

72a + 26u = 112

Substituting the value of u from the second equation, we get:

72a + 26(76 - 77a) = 112

Expanding and simplifying, we get:

72a - 2052 + 1912a = 112

Comparing like terms, we get:

83a = 112

Dividing both sides by 83, we get:

a = 13

Now, substituting the value of a in the second equation, we get:

76u - 77(13) = 31

Simplifying, we get:

76u - 969 = 31

Adding 969 to both sides, we get:

76u = 1000

Dividing both sides by 76, we get:

u = 13

Therefore, the values of u and a are 13 and 13, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for n:

54n + 18b = 143

n = (143 - 18b) / 54

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

87(143 - 18b) / 54 - 93b = 48

Expand and simplify:

87(143 - 18b) / 54 - 93b = 48

87(143) / 54 - 87(18b) / 54 - 93b = 48

87(143) / 54 - 1694b / 54 - 93b = 48

87(143) - 1694b - 4671b = 2532

-1694b - 4671b = -2532 + 87(143)

-6365b = -2532 + 1291

b = (-2532 + 1291) / -6365

b = 1291 / -6365

b = -2 / 3

Now that we have found b, we can find n:

n = (143 - 18b) / 54

n = (143 - 18(-2/3)) / 54

n = (143 + 36) / 54

n = 181 / 54

n = 3

Therefore, the values of b and n are -2/3 and 3, respectively.

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

Correct? No

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the second equation for p:

p = (69e - 6) / 88

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

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

Expand and simplify:

53e + 485e - 46 = 103

Combine like terms:

101e - 46 = 103

Add 46 to both sides:

101e = 150

Divide by 101:

e = 1.48

Now, substitute this value for e into the expression we found for p:

p = (69e - 6) / 88

Substitute e = 1.48:

p = (69(1.48) - 6) / 88

Simplify:

p = 10.12 / 88

p = 0.115

So, the cost of electricity is $1.48 and the cost of petroleum is $0.115.

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.

CodeLlama 34B:

  To find the values of p and s that satisfy both equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for p:

p = (21 + 7s) / 18

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

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

Expand and simplify:

(51s - 129 - 168s) / 18 = 14

Combine like terms:

-117s - 129 / 18 = 14

Multiply both sides by 18:

-117s - 129 = 228

Add 129 to both sides:

-117s = 101

Divide both sides by -117:

s = -101/117

Now, substitute this value of s into the first equation to solve for p:

p = (21 + 7(-101/117)) / 18

= (21 - 77/117) / 18

= 14/18

So, the values of p and s that satisfy both equations are p = 14/18 and s = -101/117.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

59c - 34w = 84

Now, from the second equation, we have:

11c + 42w = 98

We can solve for c in the first equation:

c = (84 + 34w) / 59

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

11(84 + 34w) / 59 + 42w = 98

Expand and simplify:

11(84) / 59 + 11(34w) / 59 + 42w = 98

11(123) / 59 + 42w = 98

11(123) + 42w = 59(98)

11(123) + 42w = 5742

Now, solve for w:

42w = 5742 - 11(123)
42w = 5742 - 1353
42w = 4389

w = 4389 / 42
w = 104

Now, substitute w = 104 into the expression for c:

c = (84 + 34(104)) / 59
c = (84 + 3528) / 59
c = 3612 / 59
c = 62

Therefore, c = 62 and w = 104.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we can solve for f:

f = (101 - 42z) / 45

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

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

Expand and simplify:

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

Combine like terms:

58z = 13 + 42(101/45)

z = (13 + 42(101/45)) / 58

Now, solve for z:

z = (13 + 42(101/45)) / 58

z = (13 + 42(2.2)) / 58

z = (13 + 88.4) / 58

z = 9.4 / 58

z ≈ 0.16

Now that we have found z, we can find f:

f = (101 - 42z) / 45

f = (101 - 42(0.16)) / 45

f = (101 - 6.72) / 45

f = 94.28 / 45

f ≈ 2.09

Therefore, the values of f and z are f = 2.09 and z = 0.16.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for p:

26 * p - 21 * u = 6

p = 6 / 26

p = 2/13

Now, we can substitute the value of p into the second equation:

15 * p + 58 * u = 83

15 * (2/13) + 58 * u = 83

30/13 + 58 * u = 83

58 * u = 83 - 30/13

58 * u = 83 - 22/13

58 * u = 61/13

u = 61/13 / 58

u = 11/13

Therefore, the values of p and u are 2/13 and 11/13, respectively.

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

CodeLlama 34B:

  To solve for the values of n and s, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:
92n - 38s = 62

From the second equation, we have:
59n + 8s = 75

Now, we can solve for n and s by substituting the expression for n in terms of s from the first equation into the second equation:

59(92/38) - 8s = 75

Now, we can solve for s:

s = 75 - 59(92/38)
s = 75 - 59(2.42)
s = 75 - 136.38
s = -61.38

Now, we can find n by substituting the value of s into the first equation:

92n - 38(-61.38) = 62
92n + 2341.36 = 62
92n = 62 - 2341.36
92n = -2239.36

Now, we can solve for n:

n = -2239.36 / 92
n = -24.53

So, the values of n and s are n = -24.53 and s = -61.38.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for z:

z = (63 + 35e) / 87

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

81(63 + 35e) / 87 + 58e = 154

Expand and simplify:

531 + 297e = 154e

Subtract 297e from both sides:

234 = 137e

Now, divide both sides by 137:

e = 234 / 137

e = 1.71

Now that we have found e, we can find z:

z = (63 + 35e) / 87

z = (63 + 35(1.71)) / 87

z = 24.35

Therefore, the values for e and z are e = 1.71 and z = 24.35.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for t:

t = (110 - 44h) / 11

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

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

Expand and simplify:

980 - 44h - 36h = 18

Combine like terms:

52h = 78

Divide by 52:

h = 1.5

Now, substitute h into the first equation to solve for t:

t = (110 - 44h) / 11
= (110 - 44(1.5)) / 11
= 110 - 66 / 11
= 110 - 6
= 104

Therefore, h = 1.5 and t = 104.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for b:

b = (55 + 50o) / 69

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

(41o + 18(55 + 50o)) / 69 = 85

Expand and simplify:

(41o + 860 + 90o) / 69 = 85

Combine like terms:

121o + 860 / 69 = 85

Now, solve for o:

o = (860 - 85(69)) / 121

o = (-540) / 121

o = -4.5

Now, substitute this value of o into the first equation to find b:

b = (55 + 50(-4.5)) / 69

b = (-225) / 69

b = -3.29

Therefore, the values of b and o are b = -3.29 and o = -4.5.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for q:

q = (65 + 80p) / 67

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

6q + 5p = 177

Now we have a linear equation in p and q, which we can solve using substitution or elimination. Let's use substitution again.

First, solve the second equation for p:

p = (177 - 6q) / 5

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

67q - 80p = 65

Now we have a linear equation in q, which we can solve for q.

q = 65 / 67

Now we can find p by substituting this value for q into the expression we found earlier:

p = (177 - 6(65/67)) / 5

p = 11/5

So, the values of p and q are 11/5 and 65/67, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for k:

k = (161 - 48f) / 10

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

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

Expand and simplify:

4973 - 1652f - 132f = 3100

Combine like terms:

3341 - 1782f = 3100

Add 1782f to both sides:

5123 = 3100 + 1782f

Subtract 3100 from both sides:

2023 = 1782f

Divide both sides by 1782:

f = 2023 / 1782

f = 1.139

Now, substitute this value of f into the first equation to solve for k:

k = (161 - 48(1.139)) / 10

k = (161 - 55.032) / 10

k = 105.968 / 10

k = 10.5968

Therefore, the values of k and f that satisfy the system of equations are k = 10.5968 and f = 1.139.

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

CodeLlama 34B:

  To solve this system of equations, we can start by solving the first equation for l:

31 = 58 * l - n

We can solve for l by adding n to both sides of the equation:

31 + n = 58 * l

Now, we can divide both sides of the equation by 58 to solve for l:

l = (31 + n) / 58

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

103 = n + 73 * (31 + n) / 58

We can simplify this equation by combining like terms:

103 = n + 73 * 31 / 58 + 73 * n / 58

We can simplify this equation further by combining the fractions:

103 = n + 2243 / 58

Now, we can solve for n by subtracting 2243 / 58 from both sides of the equation:

n = 103 - 2243 / 58

n = 103 - 39

n = 64

Now that we have found the value of n, we can substitute it into the expression for l that we derived earlier:

l = (31 + 64) / 58

l = 95 / 58

l = 1.63636363636364

Therefore, the values of l and n are 1.63636363636364 and 64, respectively.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for y:

29y - 28j = 39

y = (39 + 28j) / 29

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

25(39 + 28j) / 29 + 37j = 116

Expand and simplify:

940 + 828j / 29 = 116

Now, solve for j:

828j / 29 = 22

j = 22 / 828

j = 1/38

Now, substitute this value of j into the expression for y:

y = (39 + 28(1/38)) / 29

y = 39 / 29

y = 1

So, y = 1 and j = 1/38.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for u:

93u - 85a = 74
93u = 74 + 85a
u = 74/93 + 85a/93

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

96u + 17a = 186
96(74/93 + 85a/93) + 17a = 186
728/93 + 153a/93 = 186
153a/93 = 186 - 728/93
153a = 186(93) - 728
153a = 17,442 - 728
153a = 16,714
a = 16,714/153
a = 110

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

u = 74/93 + 85(110)/93
u = 74/93 + 9,350/93
u = 74/93 + 100
u = 174/93

Therefore, u = 174/93 and a = 110.

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

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for u:

u = 15 / 97

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

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

Now we can simplify and solve for g:

g = (186 - 85 * 15 / 97) / 23

g = (186 - 126.75) / 23

g = 3.25

So, u = 15 / 97 and g = 3.25.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for r:

r = (103 - 67b) / 17

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

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

Expand and simplify:

8503 - 5805b + 119b = 187

Combine like terms:

2698 - 5805b = 187

Add 5805b to both sides:

5805b = 2698 - 187

5805b = 2511

Divide both sides by 5805:

b = 2511 / 5805

b ≈ 0.435

Now, substitute this value of b into the first equation to solve for r:

r = (103 - 67(0.435)) / 17

r ≈ 1.87

So, the values of r and b that satisfy the system of equations are r ≈ 1.87 and b ≈ 0.435.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for n:

n = (41 + 54t) / 85

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

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

Expand and simplify:

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

Combine like terms:

38t + 1260 + 156t = 10850

Subtract 1260:

38t + 156t = 9590

Combine like terms:

54t = 9590 - 1260

54t = 8330

Divide by 54:

t = 155

Now that we have found t, we can substitute it into one of the original equations to find n:

n = (41 + 54t) / 85
n = (41 + 54(155)) / 85
n = (41 + 8475) / 85
n = 851 / 85
n = 10

Therefore, t = 155 and n = 10.

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.

CodeLlama 34B:

  To solve this system of equations, we can start by using the first equation to solve for u:

1) 75u - 69q = 5

We can solve for u by adding 69q to both sides of the equation:

1) 75u = 5 + 69q

Now, we can divide both sides of the equation by 75 to solve for u:

1) u = (5 + 69q) / 75

Next, we can use the second equation to solve for q:

2) 48u + 25q = 140

We can solve for q by subtracting 48u from both sides of the equation:

2) 25q = 140 - 48u

Now, we can divide both sides of the equation by 25 to solve for q:

2) q = (140 - 48u) / 25

Now that we have expressions for both u and q in terms of each other, we can substitute one of these expressions into the other equation to solve for the remaining variable. For example, we can substitute the expression for u in terms of q into the first equation:

1) 75u - 69q = 5

Now, we can substitute the expression for q in terms of u into the second equation:

2) 48u + 25q = 140

Now, we have two equations and two unknowns, and we can solve for both u and q simultaneously.

Therefore, the values of u and q that satisfy the system of equations are:

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

### Answer: u = 11/75, q = 13/25.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for v:

v = (149 - 17x) / 20

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

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

Expand and simplify:

24x - 49(149 - 17x) = 490

Combine like terms:

24x - 733 = 490

Add 733 to both sides:

24x = 1220

Divide by 24:

x = 50

Now that we have found x, we can substitute it into the first equation to find v:

v = (149 - 17x) / 20
= (149 - 17(50)) / 20
= -119 / 20
= -6

Therefore, the values of v and x are v = -6 and x = 50.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for t:

t = (147 - 41g) / 39

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

94(147 - 41g) / 39 - 91g = 42

Expand and simplify:

147 - 41g = 42 + 91g

Add 41g to both sides:

188 - 41g = 42 + 91g

Subtract 42 from both sides:

146 - 41g = 91g

Subtract 91g from both sides:

55 = 39g

Now, divide both sides by 39:

g = 55 / 39

g = 1.41

Now that we have found g, we can substitute it into the first equation to find t:

t = (147 - 41(1.41)) / 39

t = (147 - 59.41) / 39

t = 87.59 / 39

t = 2.25

Therefore, the values of t and g are 2.25 and 1.41, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for c:

c = (112 - 55o) / 6

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

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

Expand and simplify:

3300 - 3090o + 55o^2 - 48o = 36

Combine like terms:

-710o + 55o^2 = 36

Factor the left-hand side:

(7o - 11)(o + 3) = 0

Now, we have two possible solutions:

1. o = 3:

Substitute this value into the first equation:

6c + 55(3) = 112

c = 16

2. o = -11/7:

Substitute this value into the first equation:

6c + 55(-11/7) = 112

c = -12/7

Therefore, the values of c and o that satisfy the system of equations are c = 16 and o = 3, or c = -12/7 and o = -11/7.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for u:

u = (170 - 8w) / 68

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

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

Expand and simplify:

71w - 94(170/68) + 94(8w/68) = 8

71w - 94(2) + 94(8w/68) = 8

71w - 188 + 75.2w = 8

71w - 188 + 75.2w = 8

71w - 112.8w = -180

-41.8w = -180

w = 41.8/41.8 = 1

Now that we have found w, we can substitute it into the first equation to find u:

u = (170 - 8w) / 68
= (170 - 8(1)) / 68
= 162 / 68
= 2.37

So, the values of u and w that satisfy the system of equations are u = 2.37 and w = 1.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for r:

r = (92 - 8f) / 68

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

97f + 38(92 - 8f) / 68 = 182

Expand and simplify:

97f + 3392 - 296f = 182

Combine like terms:

68f = 144

f = 2

Now that we have found f, we can substitute it into one of the original equations to find r:

r = (92 - 8f) / 68
r = (92 - 16) / 68
r = 76 / 68
r = 1

Therefore, the values of r and f are 1 and 2, respectively.

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).

CodeLlama 34B:

  To solve this problem, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for d:

67d - 37r = 50

d = (50 + 37r) / 67

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

39r - 21(50 + 37r) / 67 = 16

Expand and simplify:

39r - 21(50) / 67 - 21(37r) / 67 = 16

39r - 105 - 21r = 16

-21r = -89

r = 4

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

d = (50 + 37r) / 67
= (50 + 37(4)) / 67
= (50 + 148) / 67
= 198 / 67
= 3

So, the cost of each apple is $3, and the cost of each ragdoll is $4.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

163 = 50x + a

Substituting this into the second equation, we get:

24 = 98x - 84a

Now, we can solve for x and a.

First, let's solve for x:

24 = 98x - 84a
98x = 24 + 84a
x = 24/98 + 84a/98
x = 25/98 + 84a/98

Now, let's solve for a:

163 = 50x + a
163 = 50(25/98 + 84a/98) + a
163 = 1250/98 + 420a/98 + a
163 = 1670/98 + a

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

a = 163 - 1670/98
a = 163 - 17
a = 146/98

So, the values of x and a are:

x = 25/98 + 84(146/98)/98
x = 25/98 + 1312/98
x = 156/98

Therefore, the values of x and a are x = 156/98 and a = 146/98.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for p:

p = (110 - 18b) / 67

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

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

Expand and simplify:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

82b - 44(110) / 67 + 44(18

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

63c - 36e = 27

From the second equation, we have:

8c + 32e = 69

Now, we can solve for c and e by substituting the expression for 63c - 36e in terms of c and e from the first equation into the second equation:

8c + 32e = 69

Substituting 63c - 36e = 27, we get:

8c + 32e = 69
8c + 32e = 69

Now, we can solve for c and e by adding 32e to both sides of the equation:

8c + 64e = 69 + 32e
8c + 64e = 101

Now, we can solve for c by subtracting 64e from both sides of the equation:

8c = 101 - 64e
8c = 37 - 64e

Now, we can solve for e by dividing both sides of the equation by 8:

e = (37 - 64e) / 8
e = 37/8 - 64/8
e = 4 - 8
e = -4

Now, we can find c by substituting e = -4 into the equation 8c = 37 - 64e:

8c = 37 - 64(-4)
8c = 37 - 256
8c = -219

Therefore, c = -219/8
c = -27

So, c = -27 and e = -4.

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

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for x:

26x + 29p = 107

Subtracting 29p from both sides gives us:

26x = 107 - 29p

Now, we can solve the second equation for p:

61x - 51p = 4

Adding 51p to both sides gives us:

61x = 4 + 51p

Now, we can substitute the expression for 26x in terms of p from the first equation into the second equation:

61(107 - 29p) = 4 + 51p

Expanding and simplifying, we get:

6873 - 1823p = 4 + 51p

Subtracting 4 from both sides gives us:

6869 - 1823p = 51p

Subtracting 51p from both sides gives us:

6818 = 1302p

Dividing both sides by 1302 gives us:

p = 5.23

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

26x + 29p = 107

Substituting p = 5.23, we get:

26x + 29(5.23) = 107

Simplifying, we get:

26x + 150.77 = 107

Subtracting 150.77 from both sides gives us:

26x = 56.23

Dividing both sides by 26 gives us:

x = 2.12

Therefore, the values of x and p are x = 2.12 and p = 5.23.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for l:

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

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

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

Expand and simplify:

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

Combine like terms:

31 * g - 680 / 17 + 290 * g / 17 = 17

Simplify:

10 * g - 680 / 17 = 17

Multiply by 17:

10 * g - 1176 = 259

Add 1176 to both sides:

10 * g = 1435

Divide by 10:

g = 143.5

Now that we have found g, we can find l:

l = (68 - (29 * 143.5)) / 17

l = (68 - 4201.75) / 17

l = -4133.75 / 17

l = -243.16

So, g = 143.5 and l = -243.16.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for a:

a = 20 / 33

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

24(20/33) - 26c = 29

Expand and simplify:

480/33 - 26c = 29

480 - 26c = 29(33)

480 - 26c = 99

Now, we can solve for c:

26c = 480 - 99

26c = 381

c = 381/26

c = 14 3/26

So, the values for a and c are a = 20/33 and c = 14 3/26.

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.

CodeLlama 34B:

  Sure, I can help you with that! To solve this system of equations, we need to find the values of d and j that make both equations true.

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

71d + 9j = 132

Subtracting 9j from both sides gives us:

71d = 132 - 9j

Now, we can solve for d:

d = (132 - 9j) / 71

Next, let's solve the second equation for j:

43j - 84d = 91

Adding 84d to both sides gives us:

43j = 91 + 84d

Now, we can solve for j:

j = (91 + 84d) / 43

Now that we have expressions for both d and j in terms of each other, we can substitute one expression into the other to find a single expression for one of the variables in terms of the other.

Let's substitute the expression for d in terms of j into the expression for j in terms of d:

j = (91 + 84d) / 43

Substituting the expression for d in terms of j gives us:

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

Now, we can simplify this expression by combining like terms:

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

j = (91 + 1152/71 - 756/71) / 43

j = (91 + 416/71) / 43

j = 21/71

Now that we have found the value of j, we can substitute it back into one of the original equations to find the value of d:

d = (132 - 9j) / 71

Substituting j = 21/71 gives us:

d = (132 - 9(21/71)) / 71

d = (132 - 189/71) / 71

d = 43/71

Therefore, the values of d and j that satisfy both equations are d = 43/71 and j = 21/71.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for o:

o = (163 - 26n) / 81

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

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

Expand and simplify:

87n + 23(163 - 26n) = 143(81)
87n + 3819 - 65n = 1163
154n = 1054
n = 1054 / 154
n = 7

Now that we have found n, we can find o:

o = (163 - 26n) / 81
o = (163 - 26(7)) / 81
o = (163 - 178) / 81
o = -15 / 81
o = -1 / 5

Therefore, the values of o and n are -1/5 and 7, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for w:

w = (2 + 61s) / 46

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

61s + (67 / 46) (2 + 61s) = 178

Expand and simplify:

61s + 67s + 137 = 178

Combine like terms:

128s = 41

Divide by 128:

s = 41 / 128

Now, substitute this value for s into the first equation to solve for w:

w = (2 + 61(41 / 128)) / 46

w = (2 + 249 / 128) / 46

w = 46 / 128

Therefore, the solution to the system of equations is s = 41 / 128 and w = 46 / 128.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for k:

k = (86 + 8i) / 51

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

39i + 8(86 + 8i) / 51 = 193

Expand and simplify:

39i + 672 + 64i = 193

Combine like terms:

106i + 672 = 193

Subtract 672 from both sides:

106i = 121

Divide both sides by 106:

i = 11

Now that we have the value of i, we can substitute it into one of the original equations to solve for k:

k = (86 + 8i) / 51
= (86 + 8(11)) / 51
= (86 + 88) / 51
= 174 / 51
= 3

Therefore, the values of i and k are i = 11 and k = 3.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for m:

m = (146 - 17l) / 26

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

93((146 - 17l) / 26) + l = 126

Expand and simplify:

93(146/26) - 93(17l/26) + l = 126

Combine like terms:

93(146/26) - 1591l/26 + l = 126

Simplify:

93(146/26) - 1755l/26 = 126 - 146/26

Simplify further:

93(146/26) - 1755l/26 = 126 - 5

Now, we can solve for l:

1755l/26 = 121

l = 121(26) / 1755

l = 26 / 1755

Now, we can find m:

m = (146 - 17l) / 26

m = (146 - 17(26/1755)) / 26

m = (146 - 426/1755) / 26

m = 104/1755

Therefore, the values of l and m are 26/1755 and 104/1755, respectively.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

8f + 39h = 66

Substituting the value of 8f from the second equation, we get:

29(66/8) + 46h = 119

Simplifying, we get:

29(8) + 46h = 119

Subtracting 29(8) from both sides, we get:

46h = 90

Dividing both sides by 46, we get:

h = 2

Now, we can find f by substituting the value of h in either of the two equations:

8f + 39(2) = 66

Solving for f, we get:

8f = 66 - 78

8f = -12

f = -12/8

f = -1.5

Therefore, the values of h and f are 2 and -1.5, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the second equation for b:

b = (14 - 62k) / 69

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

22b + 23k = 109

Substituting the expression for b in terms of k, we get:

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

Expanding and simplifying, we get:

-1338k + 3796 = 0

Solving for k, we get:

k = 3796 / -1338 = -2.8

Now, we can find b by substituting this value of k into the expression we found earlier:

b = (14 - 62(-2.8)) / 69 = 14 / 69 = 0.2

Therefore, the values of k and b that satisfy the system of equations are k = -2.8 and b = 0.2.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we can solve for s:

s = 1 + 55/84m

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

63m - 2(1 + 55/84m) = 98

Expand and simplify:

63m - 2 - 110/84m = 98

Multiply both sides by 84m:

504m - 168 - 110 = 792m

Subtract 168 from both sides:

336m - 110 = 792m

Add 110 to both sides:

446m = 902m

Divide both sides by 446:

m = 902/446

m = 2

Now that we have found m, we can substitute it into the expression for s from the first equation:

s = 1 + 55/84m

s = 1 + 55/84(2)

s = 1 + 27.75

s = 38.75

Therefore, the values of m and s are 2 and 38.75, respectively.

### Answer: m = 2, s = 38.75.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for b:

b = 105 / 6
b = 17.5

Now, substitute the value of b into the second equation:

(95 * k) - (51 * 17.5) = 67
(95 * k) - 862.5 = 67
95k - 862.5 = 67
95k = 939.5
k = 939.5 / 95
k = 9.8

Therefore, the values of b and k are 17.5 and 9.8, respectively.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for d:

d = (114 - 62u) / 33

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

32u + 40((114 - 62u) / 33) = 83

Expand and simplify:

32u + 40(114/33 - 62u/33) = 83

Combine like terms:

32u - 244u + 2520 = 83

Simplify:

-212u + 2520 = 83

Solve for u:

u = (2520 - 83) / -212

u = 12

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

d = (114 - 62u) / 33

d = (114 - 62(12)) / 33

d = 12

Therefore, the values of d and u are 12 and 12, respectively.

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

CodeLlama 34B:

  Sure! To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for c:

c = (102 - 28p) / 5

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

20(102 - 28p) / 5 - 67p = 13

Expand and simplify:

2010 - 560p - 1340p + 170p^2 = 13

Combine like terms:

170p^2 - 700p - 1970 = 0

Now, we can factor the left-hand side:

(17p - 30)(17p + 68) = 0

So, we have two possible solutions:

17p - 30 = 0 or 17p + 68 = 0

Solving for p:

p = 30/17 or p = -68/17

Now, we can substitute these values back into the original equation to find the corresponding values of c:

For p = 30/17, c = (102 - 28(30/17)) / 5 = 12

For p = -68/17, c = (102 - 28(-68/17)) / 5 = 24

Therefore, the values of c and p are 12 and 30/17, or 24 and -68/17.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for r:

r = (147 - 12q) / 58

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

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

Expand and simplify:

97q - 76(147) / 58 + 912q = 76

Combine like terms:

194q - 76 = 76

Add 76 to both sides:

194q = 152

Divide both sides by 194:

q = 152 / 194

q = 7/11

Now that we have the value of q, we can substitute it into the first equation to solve for r:

r = (147 - 12q) / 58

Substitute q = 7/11:

r = (147 - 12(7/11)) / 58

Expand and simplify:

r = (147 - 84/11) / 58

Combine like terms:

r = 63/11

r = 5/2

Therefore, the values of r and q are 5/2 and 7/11, respectively.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for v:

v = 10 / 47

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

73 * (10 / 47) + 2 * k = 128

Now we can simplify and solve for k:

730 / 47 + 2 * k = 128

2 * k = 128 - 730 / 47

2 * k = -643 / 47

k = -321 / 94

Now we can find v by substituting the expression for k into the first equation:

v = 10 / 47

So, the solution to the system of equations is v = 10/47 and k = -321/94.

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?

CodeLlama 34B:

  To solve this system of equations, we can start by using the first equation to solve for p:

89p - 41q = 60

We can solve for p by adding 41q to both sides of the equation:

89p = 60 + 41q

Now, we can use the second equation to solve for q:

27p + 91q = 124

We can solve for q by subtracting 27p from both sides of the equation:

91q = 124 - 27p

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

89p - 41(124 - 27p) = 60

Simplifying and solving for p, we get:

89p = 60 + 41(124 - 27p)

p = 60/89

Now, we can substitute the value of p into the second equation to solve for q:

27(60/89) + 91q = 124

Simplifying and solving for q, we get:

q = 124 - 27(60/89)

q = 124 - 27(60/89)

q = 124 - 162/89

q = 124 - 18/9

q = 124 - 2

q = 122

Therefore, the values of p and q are p = 60/89 and q = 122.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

88u - 96d = 12

Now, from the second equation, we have:

27u + 36d = 71

We can solve for u in the first equation:

u = 12 / 88

Now, substitute this value of u into the second equation:

27(12/88) + 36d = 71

Expand and simplify:

324/88 + 36d = 71

324/88 = 71 - 36d

Now, solve for d:

d = (71 - 324/88) / 36

d = (71 - 324/88) / 36

d = (71 - 324/88) / 36

Now, substitute this value of d into the first equation:

88u - 96d = 12

88(12/88) - 96(71 - 324/88) = 12

88(12/88) - 96(71 - 324/88) = 12

88(12/88) - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

12 - 96(71 - 324/88) = 12

Now, simplify:

12 - 96(71 -

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

20n - 18f = 9

Now, from the second equation, we have:

3n - 2f = 70

We can solve for f in terms of n by adding the two equations:

20n - 18f + 3n - 2f = 9 + 70

Combine like terms:

23n - 20f = 79

Now, we can solve for f by dividing both sides by 23:

f = (79 + 20f) / 23

f = 79 / 23 + f / 23

f = 3 + f / 23

Now, we can solve for f by substituting f = 3 + f / 23 into the first equation:

20n - 18(3 + f / 23) = 9

Expand and simplify:

20n - 54 - 18f / 23 = 9

Combine like terms:

20n - 54 - 18f = 9 + 18f / 23

Simplify:

20n - 54 - 18f = 9 + 18f / 23

Now, we can solve for n by substituting n = (9 + 18f / 23) / 20 into the second equation:

3(9 + 18f / 23) - 2f = 70

Expand and simplify:

27 + 54f / 23 - 2f = 70

Combine like terms:

27 + 52f / 23 = 70

Now, we can solve for f by substituting f = (70 - 27 - 52f / 23) / 2 into the first equation:

20n - 18(70 - 27 - 52f / 23) = 9

Expand and simplify:

20n - 1260 + 126f = 9

Combine like terms:

20n - 1260 + 126f = 9

Now, we can solve for n by substituting n = (9 + 126f) / 20 into the second equation:

3(9 + 126f) - 2f = 70

Expand and simplify:

27 + 378f - 2f = 70

Combine like terms:

27 + 376f = 70

Now, we can solve for f by substituting f = (70 - 27) / 376 into the first equation:

20n - 18(70 - 27) / 376 = 9

Expand and simplify:

20n - 1260 + 18f = 9

Combine like terms:

20n - 1260 + 18f = 9

Now, we can solve for n by substituting n = (9 + 18f) / 20 into the second equation:

3(9 + 18f) - 2f = 70

Expand and simplify:

27 + 54f - 2f = 70

Combine like terms:

27 + 52f = 70

Now, we can solve for f by substituting f = (70 - 27) / 52 into the first equation:

20n - 18(70 - 27) / 52 = 9

Expand and simplify:

20n - 1260 + 18f = 9

Combine like terms:

20n - 1260 + 18f = 9

Now, we can solve for n by substituting n = (9 + 18f

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for j:

j = (133 - 7l) / 97

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

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

Expand and simplify:

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

Combine like terms:

22(133) / 97 + 37l = 76

Subtract 22(133) / 97 from both sides:

37l = 76 - 22(133) / 97

Solve for l:

l = (76 - 22(133) / 97) / 37

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

j = (133 - 7l) / 97

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

Simplify:

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

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

j = (133 - 504) / 97

j = -371 / 97

Therefore, the values of j and l are -371/97 and 76 - 22(133) / 97, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for d:

d = (53 + 46f) / 21

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

8(53 + 46f) / 21 + 84f = 133

Expand and simplify:

408 + 344f = 133

Subtract 408 from both sides:

-84f = -275

Divide both sides by -84:

f = 3.25

Now, substitute this value of f into the first equation to solve for d:

d = (53 + 46(3.25)) / 21

d = (53 + 142.5) / 21

d = 195.5 / 21

d = 9

Therefore, the values of d and f are 9 and 3.25, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for u:

u = (116 - 11w) / 74

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

66((116 - 11w) / 74) - 68w = 21

Expand and simplify:

66(116 - 11w) / 74 - 68w = 21

66(116) / 74 - 68w = 21

796 - 68w = 21

68w = 775

w = 11

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

u = (116 - 11w) / 74
= (116 - 11(11)) / 74
= (116 - 121) / 74
= -6 / 74

Therefore, the values of u and w that satisfy the system of equations are u = -6/74 and w = 11.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for f:

f = (96 + 42j) / 76

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

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

Expand and simplify:

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

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

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

Now, solve for j:

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96) / 76) / 47

j = (136 - 34(96

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for u:

u = (174 - 32e) / 68

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

63e - 69((174 - 32e) / 68) = 1

Expand and simplify:

63e - 69(174/68 - 32e/68) = 1

63e - 69(2 - 32e/68) = 1

63e - 138 + 21e = 1

45e = 149

e = 3

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

u = (174 - 32e) / 68
= (174 - 32(3)) / 68
= (174 - 96) / 68
= 78 / 68
= 1

Therefore, u = 1 and e = 3.

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.

CodeLlama 34B:

  To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for p:

p = (129 - 4n) / 57

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

(129 - 4n) / 57 + 39n = 154

Now, simplify and solve for n:

129 - 4n + 39n = 154

n = 129 / 43

Now, substitute this value of n into one of the original equations to find p:

57p + 4(129/43) = 129

p = (129 - 4(129/43)) / 57

p = 23/57

Therefore, the values of p and n that satisfy the system of linear equations are p = 23/57 and n = 129/43.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for z:

z = (32 + 44y) / 66

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

60y + 14(32 + 44y) / 66 = 116

Expand and simplify:

60y + 14(32) / 66 + 14(44y) / 66 = 116

60y + 896 / 66 + 14(44y) / 66 = 116

60y + 896 / 66 + 624y / 66 = 116

60y + 1520 / 66 = 116

60y = 116 - 1520 / 66

60y = -454 / 66

y = -7.5

Now that we have found y, we can substitute it into one of the original equations to find z:

z = (32 + 44(-7.5)) / 66

z = (32 - 322.5) / 66

z = -322.5 / 66

z = -5

Therefore, the values of y and z are y = -7.5 and z = -5.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for t:

t = (45 + 58h) / 83

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

69h + 11(45 + 58h) / 83 = 124

Now simplify and solve for h:

69h + 11(45) / 83 = 124
69h + 5 = 124
69h = 119
h = 119 / 69
h = 1.75

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

t = (45 + 58h) / 83
t = (45 + 58(1.75)) / 83
t = 45 / 83 + 58 / 83
t = 53 / 83

Therefore, the solution to the system of equations is t = 53/83 and h = 1.75.

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?

CodeLlama 34B:

  To solve this system of equations, we can start by solving the first equation for h:

h = (9 + 61o) / 79

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

(16 * (9 + 61o) / 79) - 12o = 9

Expand and simplify:

(144 + 1192o) / 79 - 12o = 9

Combine like terms:

1331o / 79 = 9

Multiply both sides by 79:

1331o = 683

o = 683 / 1331 ≈ 0.51

Now, substitute this value of o into the first equation to solve for h:

h = (9 + 61(683 / 1331)) / 79 ≈ 1.37

Therefore, the values of o and h are approximately 0.51 and 1.37, respectively.

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

CodeLlama 34B:

  To solve for the variables s and y, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for y:

y = (139 - 56s) / 4

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

65 * ((139 - 56s) / 4) - 90 * s = 16

Expand and simplify:

65 * 139 / 4 - 65 * 56s / 4 - 90 * s = 16

Combine like terms:

65 * 139 / 4 - 65 * 56s / 4 - 90 * s = 16

Simplify:

1987 - 344s - 90s = 16

Combine like terms:

1987 - 434s = 16

Add 434s to both sides:

1987 = 450s

Divide both sides by 450:

s = 1987 / 450

s = 4

Now that we have found s, we can substitute it into the first equation to find y:

y = (139 - 56s) / 4

y = (139 - 56(4)) / 4

y = (139 - 224) / 4

y = -85 / 4

y = -21

Therefore, the values of s and y that satisfy the system of equations are s = 4 and y = -21.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for d:

d = 75 / 42
d = 1.79

Now, we can substitute this value of d into the second equation:

40 * 1.79 + 45 * z = 162
79.6 + 45 * z = 162
45 * z = 82.4
z = 1.82

So, the values of d and z are 1.79 and 1.82, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for 'o':

(42 * o) + (24 * a) = 142

Subtracting 24a from both sides gives us:

38 * o = 142 - 24a

Dividing both sides by 38 gives us:

o = (142 - 24a) / 38

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

(42 * a) + (6 * (142 - 24a)) = 75

Expanding the right-hand side gives us:

42a + 6(142 - 24a) = 75

Simplifying the expression gives us:

42a + 6(142) - 6(24a) = 75

Combining like terms gives us:

42a + 844 - 144a = 75

Subtracting 844 from both sides gives us:

-100a = -799

Dividing both sides by -100 gives us:

a = 7.99

Now that we have found the value of 'a', we can substitute it into the expression for 'o' to find its value:

o = (142 - 24(7.99)) / 38

Substituting the value of 'a' gives us:

o = (142 - 174.64) / 38

Simplifying the expression gives us:

o = -32.64 / 38

Subtracting 32.64 from both sides gives us:

-32.64 = -32.64 / 38

Multiplying both sides by 38 gives us:

-32.64 = -32.64

Therefore, the values of 'a' and 'o' are 7.99 and -32.64, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for r:

r = 45 / 39

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

16*p - 84*(45/39) = 36

Expand and simplify:

16*p - 360 = 36

Add 360 to both sides:

16*p = 396

Divide both sides by 16:

p = 24

Now, substitute the value of p into the first equation to find r:

39*r - 2*24 = 45

Expand and simplify:

39*r - 48 = 45

Add 48 to both sides:

39*r = 93

Divide both sides by 39:

r = 2

Therefore, the values of p and r are 24 and 2, respectively.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

23d - 52w = 7

Now, from the second equation, we have:

64w - 8d = 58

We can solve for 'd' in the first equation:

d = (7 + 52w) / 23

Now, substitute this expression for 'd' in the second equation:

64w - 8((7 + 52w) / 23) = 58

Now, simplify and solve for 'w':

64w - 8(7 + 52w) / 23 = 58

64w - 8(7) / 23 - 8(52w) / 23 = 58

64w - 56 / 23 - 416w / 23 = 58

64w - 462 / 23 = 58

64w = 58 + 462 / 23

64w = 104 / 23

w = 104 / (23 \* 64)

w = 104 / 1472

w = 1 / 14

Now, substitute this value of 'w' in the first equation to find 'd':

d = (7 + 52(1/14)) / 23

d = (7 + 78 / 14) / 23

d = (7 + 5) / 23

d = 12 / 23

So, the values of 'd' and 'w' are 12/23 and 1/14, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for z:

z = 184 / 71

z = 2.59

Next, we can substitute the value of z into the second equation:

(52 * 2.59) - (47 * n) = 19

115.38 - (47 * n) = 19

47 * n = 66.38

n = 66.38 / 47

n = 1.41

Now we have the values of n and z:

n = 1.41
z = 2.59

Therefore, the solution to the system of equations is n = 1.41 and z = 2.59.

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

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for e:

e = (189 - 90z) / 70

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

99z - 84(189 - 90z) / 70 = 20

Expand and simplify:

99z - 1632 + 726z = 20

Combine like terms:

172z = 20

Divide by 172:

z = 20 / 172

Now, solve for e:

e = (189 - 90z) / 70

Substitute the value of z:

e = (189 - 90(20 / 172)) / 70

Simplify:

e = (189 - 90(20 / 172)) / 70

e = (189 - 90(1 / 9)) / 70

e = (189 - 11) / 70

e = 178 / 70

e = 2

Therefore, the values of e and z are 2 and 20/172, respectively.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

From the first equation, we have:

26o - 44f = 95

Subtracting 44f from both sides gives us:

26o = 95 + 44f

Subtracting 26o from both sides gives us:

-26o = -95 - 44f

Dividing both sides by -26 gives us:

o = (95 + 44f) / -26

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

87f + 11(95 + 44f) / -26 = 169

Expanding and simplifying, we get:

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

87f + 11(95) / -26 + 11(44f) / -26 = 169

Expected answer: {f: 3349/2746, o: 15701/2746}

Correct? No

Problem: Calculate the values of z and p using the following system of equations: 40*z - 20*p = 51 6*z + 58*p = 165.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, solve the first equation for z:

z = (51 + 20p) / 40

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

6(51 + 20p) / 40 + 58p = 165

Expand and simplify:

306 + 120p = 165

Subtract 306 from both sides:

120p = -141

Divide both sides by 120:

p = -141/120

Now, solve for z:

z = (51 + 20p) / 40
= (51 - 28) / 40
= 23 / 40

So, z is equal to 23/40 and p is equal to -141/120.

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.

CodeLlama 34B:

  To solve this system of equations, we can use substitution or elimination. Let's use substitution.

First, we can solve the first equation for s:

s = (5 + 89f) / 71

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

(3f + 10(5 + 89f)) / 71 = 93

Expand and simplify:

(3f + 50f + 890) / 71 = 93

Combine like terms:

83f / 71 = 93

Multiply both sides by 71:

83f = 93 \* 71

83f = 6,503

f = 6,503 / 83

f = 78

Now that we have found f, we can find s:

s = (5 + 89f) / 71

s = (5 + 89(78)) / 71

s = (5 + 6,682) / 71

s = 6,687 / 71

s = 95

Therefore, the values of s and f are 95 and 78, respectively.

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

Correct? No