Answer
(-2, -1) or (-6, 3)
Work Step by Step
x + y = -3 can be written as x = -3 - y. Plug this into $x^{2} + 2y^{2} = 12y + 18$
$(-3 - y)^{2} + 2y^{2} = 12y + 18$
$9 + 6y + y^{2} + 2y^{2} = 12y + 18$
$-9 - 6y +3y^{2} = 0$
Divide both sides by 3
$-3 - 2y +y^{2} = 0$
(y + 1)(y - 3) = 0
y = -1 or 3
Plug y-values into x = -3 - y
x = -3 + 1 = -2
x = -3 - 3 = -6
(-2, -1) or (-6, 3)
