3x + 4y = 5
3x - 4y = -11 by elimination

To solve by elimination you just add the equations to "cancel out" one of the variables. In this case we would cancel out the y by adding.

3x+4y=5
+
3x-4y=-11

6x=-6
x=-1

Now, since we have our x value, we can plug it into either of the other equations to get the y value.

3(-1)+4y=5
-3+4y=5
4y=8
y=2

Your answer for this system is x=-1 and y=2