Help with a quadratic simultaneous equation.

x - 2y = 7
x² + 4y² = 37

Here's what I did (the function is in brackets):

x - 2y = 7 (+2y)
x = 2y + 7

Substituted into other equation:

(2y + 7)² + 4y² = 37

Expanded brackets:

(2y + 7)(2y+7) + 4y² = 37
4y² + 14y + 14y +49 + 4y² = 37

Simplified:

8y² + 28y + 49 = 37 (-37)
8y² + 28 + 12 = 0

Factorised:

(y + 3)(8y + 4)

y +3 = 0 (-3)
y = -3

or

8y + 4 = 0 (-4)
8y = -4 (÷8)
y = -0.5

Those are my solutions for y, but these don't give correct solutions when I substitute the results in for x, can somebody point out my mistake and explain the correct solution?

Thanks!