5x+6y=13; -5x+2y=11. how do I solve this

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