You can solve the system by isolating the same variable in both equations, then setting those equations equal to each other. For instance, say we isolate y:
[tex]4x+3y=12[/tex]
[tex]3y=12-4x[/tex]
[tex]y=4- \frac{4}{3} x[/tex]
Do the same for the other equation, then set both equations equal to each other. You can then solve for x. Once you have a value for x, you can plug it into either of the original equations and find y!