First solve one of your equations for one of the unknowns. It doesn't matter which in this case, but typically you want to solve the least complicated equation first. I will solve the top equation for "y" first:

y = -x - 9

Now insert this value of y into the second equation, then solve it for x.

(-x - 9) = -2x + 3

2x -x - 9 = 2x - 2x + 3

x - 9 = 3

x = 9 + 3 = 12.

Now insert this value for x into your solved y equation and that will give you the y value:

y = -(12) - 9 = -21.

So your solution is (x, y) = (12, -21).

-Dan