First, let's solve the second equation for y:

X + y = 3
y = 3 - x

Now, substitute y = 3 - x into the first equation:

X^2 - 3(3-x) = -9
X^2 - 9 + 3x = -9
X^2 + 3x - 9 = -9
X^2 + 3x = 0
X(X + 3) = 0

So, the solutions are X = 0 and X = -3.

Now substitute these values back into the second equation to find the corresponding values of y:

For X = 0:
y = 3 - 0
y = 3

For X = -3:
y = 3 - (-3)
y = 6

Therefore, the solutions to the system of equations are X = 0, y = 3 and X = -3, y = 6.