The answer is (3,3). To solve this, first you write the system down. 
x+3y=12
-4x+3y=-3
                         Next, you eliminate y by multiplying the bottom equation by negative 1. 
x+3y=12
-1(-4x+3y=-3)

                         Then, your answer is:
                                   x+3y=12
                                   4x-3y+3
                         Next, you combine like terms. Your answer is:
                                   5x=15. (The y’s cancel out, because 3 is the opposite of negative 3.)
                                  Divide both sides by 5, leaving you with x=3. 
                                  Lastly, you substitute x into the top equation. You get:
                                 3+3y=12. 
                               Subtract 3 from both sides, leaving you with 3y=9.
                                 Divide both sides by 3, so y=3. The final answer is (3,3).