Examine this system of linear equations. y - x = 2, x + y = 4 Which is a solution of the system of equations? (1, 3) (2, 2) (3, 1) (4, 2)

A.

Step-by-step explanation:

A. (1,3)

(1, 3)

Step-by-step explanation:

Solve the following system:

{y - x = 2 | (equation 1)

{x + y = 4 | (equation 2)

Add equation 1 to equation 2:

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

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

Divide equation 2 by 2:

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

{0 x+y = 3 | (equation 2)

Subtract equation 2 from equation 1:

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

{0 x+y = 3 | (equation 2)

Multiply equation 1 by - 1:

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

{0 x+y = 3 | (equation 2)

Collect results:

Answer: x = 1, y = 3