Solve each system of equations

2a-3b+5c=58

-5a+b-4c=-51

-6a-8b+c=22

a = 3, b = - 4, c = 8

Step-by-step explanation:

Solve the following system:

{2 a - 3 b + 5 c = 58 | (equation 1)

-5 a + b - 4 c = - 51 | (equation 2)

-6 a - 8 b + c = 22 | (equation 3)

Swap equation 1 with equation 3:

{ - (6 a) - 8 b + c = 22 | (equation 1)

- (5 a) + b - 4 c = - 51 | (equation 2)

2 a - 3 b + 5 c = 58 | (equation 3)

Subtract 5/6 * (equation 1) from equation 2:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a + (23 b) / 3 - (29 c) / 6 = - 208/3 | (equation 2)

2 a - 3 b + 5 c = 58 | (equation 3)

Multiply equation 2 by 6:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a+46 b - 29 c = - 416 | (equation 2)

2 a - 3 b + 5 c = 58 | (equation 3)

Add 1/3 * (equation 1) to equation 3:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a+46 b - 29 c = - 416 | (equation 2)

0 a - (17 b) / 3 + (16 c) / 3 = 196/3 | (equation 3)

Multiply equation 3 by 3:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a+46 b - 29 c = - 416 | (equation 2)

0 a - 17 b + 16 c = 196 | (equation 3)

Add 17/46 * (equation 2) to equation 3:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a+46 b - 29 c = - 416 | (equation 2)

0 a+0 b + (243 c) / 46 = 972/23 | (equation 3)

Multiply equation 3 by 46/243:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a+46 b - 29 c = - 416 | (equation 2)

0 a+0 b+c = 8 | (equation 3)

Add 29 * (equation 3) to equation 2:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a+46 b+0 c = - 184 | (equation 2)

0 a+0 b+c = 8 | (equation 3)

Divide equation 2 by 46:

{ - (6 a) - 8 b + c = 22 | (equation 1)

0 a+b+0 c = - 4 | (equation 2)

0 a+0 b+c = 8 | (equation 3)

Add 8 * (equation 2) to equation 1:

{ - (6 a) + 0 b+c = - 10 | (equation 1)

0 a+b+0 c = - 4 | (equation 2)

0 a+0 b+c = 8 | (equation 3)

Subtract equation 3 from equation 1:

{ - (6 a) + 0 b+0 c = - 18 | (equation 1)

0 a+b+0 c = - 4 | (equation 2)

0 a+0 b+c = 8 | (equation 3)

Divide equation 1 by - 6:

{a+0 b+0 c = 3 | (equation 1)

0 a+b+0 c = - 4 | (equation 2)

0 a+0 b+c = 8 | (equation 3)

Collect results:

Answer: {a = 3, b = - 4, c = 8