Solve by elimination

-5x+8y=-27

-8x+7y=-20

x = - 1, y = - 4

Step-by-step explanation by elimination:

Solve the following system:

{8 y - 5 x = - 27 | (equation 1)

7 y - 8 x = - 20 | (equation 2)

Swap equation 1 with equation 2:

{ - (8 x) + 7 y = - 20 | (equation 1)

- (5 x) + 8 y = - 27 | (equation 2)

Subtract 5/8 * (equation 1) from equation 2:

{ - (8 x) + 7 y = - 20 | (equation 1)

0 x + (29 y) / 8 = (-29) / 2 | (equation 2)

Multiply equation 2 by 8/29:

{ - (8 x) + 7 y = - 20 | (equation 1)

0 x+y = - 4 | (equation 2)

Subtract 7 * (equation 2) from equation 1:

{ - (8 x) + 0 y = 8 | (equation 1)

0 x+y = - 4 | (equation 2)

Divide equation 1 by - 8:

{x+0 y = - 1 | (equation 1)

0 x+y = - 4 | (equation 2)

Collect results:

Answer: {x = - 1, y = - 4