x + y = 18
x = 18 - y
x^2 = (18 - y)^2
x^2 = 324 -36y +y^2
substitue into the other equation
x^2 +2y^2 = 324
324 -36y +y^2 = 324
solve for y
-36y +y^2 = 0
(-36 +y) y = 0
y = 36 or 0
use the original equation
x +y = 18
enter the values for y
x +36 = 18 or x +0 = 18
solve for x
x = -18 or x = 18
Answer: x = -18, y = 36 or x = 18, y = 0
check
x + y = 18
-18 + 36 = 18 True
check
x + y = 18
18 + 0 = 18 True