Question

Which ondered pair is the solution to this system of equations? y=x+4 x+y=2 (1) (1,5) (2) (0,2) (3)(-1,3) (4)(-4,0)

Answer 1

Solve the following system:

{y = x + 4 | (equation 1)

y + x = 2 | (equation 2)

Express the system in standard form:

{-x + y = 4 | (equation 1)

x + y = 2 | (equation 2)

Add equation 1 to equation 2:

{-x + y = 4 | (equation 1)

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

Divide equation 2 by 2:

{-x + y = 4 | (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)

Answer: x = -1 y = 3