To solve this system of equations, we can first solve the first equation for y in terms of x:

x - y = 7
y = x - 7

Now substitute y = x - 7 into the second equation:

x^2 + (x - 7)^2 = 9 - 2x(x - 7)
x^2 + x^2 - 14x + 49 = 9 - 2x^2 + 14x
2x^2 - 14x + 49 = 9 - 2x^2 + 14x
4x^2 - 28x + 40 = 0
x^2 - 7x + 10 = 0
(x - 5)(x - 2) = 0

So x = 5 or x = 2

For x = 5, y = 5 - 7 = -2
For x = 2, y = 2 - 7 = -5

Therefore, the solutions to the system of equations are (5, -2) and (2, -5).