4x^2 -2y^2 = -2
x^2 +4y^2 = 40
multiply the top equation by 2
8x^2 -4y^2 = -4
x^2 +4y^2 = 40
add the equations
8x^2 -4y^2 = -4
x^2 +4y^2 = 40
9x^2 +0y^2 = 36
simplify
9x^2 = 36
solve for x
x^2 = 4
x = -2 or +2
pick one of the original equations
4x^2 -2y^2 = -2
enter the value for x
4((-2)^2) - 2y^2 = -2 or 4((2)^2) - 2y^2 = -2
In the line above (-2)^2 and (2)^2 both equal 4
4(4) - 2y^2 = -2
16 - 2y^2 = -2
-2y^2 = -18
y^2 = 9
y = -3 or +3
Answer: x is -2 or +2, y is -3 or +3