Solve the system of linear equations using elimination. - 2x - y = 3 - 9x - y = 17

A) (2, 1) B) (2, - 1) C) (-2, 1) D) (-2, - 1)

x = - 2, y = 1

Step-by-step explanation:

Solve the following system:

{-2 x - y = 3 | (equation 1)

-9 x - y = 17 | (equation 2)

Swap equation 1 with equation 2:

{ - (9 x) - y = 17 | (equation 1)

- (2 x) - y = 3 | (equation 2)

Subtract 2/9 * (equation 1) from equation 2:

{ - (9 x) - y = 17 | (equation 1)

0 x - (7 y) / 9 = - 7/9 | (equation 2)

Multiply equation 2 by - 9/7:

{ - (9 x) - y = 17 | (equation 1)

0 x+y = 1 | (equation 2)

Add equation 2 to equation 1:

{ - (9 x) + 0 y = 18 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by - 9:

{x+0 y = - 2 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: {x = - 2, y = 1