X - 3y = 1

3x - 5y = 11

I would isolate x in the first equation:

x = 3y + 1

For the second equation, you could just substitute the x inside:

3x - 5y = 11

3 (3y + 1) - 5y = 11

9y + 3 - 5y = 11

4y + 3 = 11

4y = 8

y = 2

Using the y = 2, we can find x.

x = 3y + 1

x = 3 (2) + 1

x = 7

x = 7 and y = 2

The answers are ...

x=7

y=2