You solve for X in one equation and plug it into the other. So...
5x+6Y=13
5x=13-6Y
x=(13-6Y)/5
Then, you replace X in the other equation...
-5x+2y=11
-5[(13-6y)/5]+2y=11
-13+6y+2y=11
8y=11+13
8y=24
y=3
Now that you have Y, you just solve for x using either equations...
5x+6(3)=13
5x=13-18
5x=-5
x=-1
Therefore, X = -1 & Y = 3