To solve this system of equations, we can use the substitution method.

From the first equation, we can solve for x in terms of y:
x = 2y + 2

Now, we can substitute this expression for x in the second equation:

3(2y + 2) - y^2 = 11
6y + 6 - y^2 = 11
y^2 - 6y - 5 = 0
(y - 5)(y + 1) = 0

So, y = 5 or y = -1.

If y = 5, then x = 2(5) + 2 = 12.
If y = -1, then x = 2(-1) + 2 = 0.

Therefore, the solutions to the system of equations are x = 12, y = 5 and x = 0, y = -1.