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