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:

{x = -2 , y = 1