x + 2y = 13
3x - 5y = 6

I'm getting lost with this problem. I started adding the two equations together and I wanted to make sure I had done it correctly

4x-3y=19
x-3y=15
I'm not sure where to go from here.

when substitution problems have 2 equations, 1 of the problems have to be solved for x or y and then substituted back into the problem?

you don't have to add/subtract equations.

first equation

x + 2y = 13

x = 13 - 2y

then take this value for x, and put it in the second equation, and solve for y.

You have :

x + 2y = 13
3x - 5y = 6

You can not solve both values for x and y at once.
You first have to eliminate either x or y in both equations.
So if we eliminate x , you need to multiply all values of equation 1 with 3, to get the value of 3x

x + 2y = 13
3 (x + 2y) = 3 . 13
3x +6y = 39
3x = 39 - 6y

Now substitute that value of 3x in the second equation (3x - 5y = 6)

39 - 6y - 5y = 6

and work out the value of y
Once you have the value of y , you can use the first equation to work out the value of x