Solve the system by using the technique of 'elimination': - 2x+5y=-42,7x+2y=30

Solve the following system using elimination:

{5 y - 2 x = - 42 | (equation 1)

7 x + 2 y = 30 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 2 y = 30 | (equation 1)

- (2 x) + 5 y = - 42 | (equation 2)

Add 2/7 * (equation 1) to equation 2:

{7 x + 2 y = 30 | (equation 1)

0 x + (39 y) / 7 = (-234) / 7 | (equation 2)

Multiply equation 2 by 7/39:

{7 x + 2 y = 30 | (equation 1)

0 x+y = - 6 | (equation 2)

Subtract 2 * (equation 2) from equation 1:

{7 x+0 y = 42 | (equation 1)

0 x+y = - 6 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 6 | (equation 1)

0 x+y = - 6 | (equation 2)

Collect results:

Answer: {x = 6, y = - 6