Can someone explain how to solve system of equations with exponents

For example"
x^2 + 4y^2 =36
x + 2y = 6

I tried substituting x = 6 - 2y
But that just gives me 36 = 36
:(

substitute 6 - 2y in the first equation for x and solve for x

(6 - 2y)^2 + 4y^2 = 36

36 - 24y + 4y^2 + 4y^2 = 36

8y^2 - 24y = 0

8(y^2 - 3y) = 0

y^2 - 3y = 0

y(y - 3) = 9

y = 0 or y = 3

replace 0 and 3 in for y in one of the original equations and solve for the corresponding x's. Let's use equation 2 and we get

for y = 0 we have x + 2(0) = 6 so x = 6

for y = 3 we have x + 2(3) = 6 so x = 0

solutions (6,0) and (0,3)

Right. That's it. The question is a true statement, and that's your final answer.