1). x + y = 2
2). x^2 + 2y = 12
in equation 1). solve for y.
1a). y = 2 - x
substitute into equation 2).
x^2 + 2(2 - x) = 12
x^2 - 2x + 4 = 12
x^2 - 2x -8 = 0
(x - 4)(x + 2) = 0
x equals x = 4 or x = -2
plug into equation 1)
x + y = 2
4 + y = 2 or -2 + y = 2
y = -2 or y = 4 in x,y notation the answers look like this:
(4, -2) or (-2, 4)
check answers in equation 2)
x^2 + 2y = 12
4^2 + 2(-2) = 12 or (-2)^2 + 2(4) = 12
8 -4 = 12 NO!!! or 4 + 8 = 12
(4, -2) is not an answer. The answer is (-2, 4).