x = 2y + 3,      (1)
3x + 5y = 1.     (2)

You just have x expressed via y in the equation (1).
So, simply substitute it for x into equation (2). You will get a single equation for y

3*(2y + 3) + 5y = 1.

Simplify and solve for y:

6y + 9 + 5y = 1,

11y = 1 - 9,

11y = -8,

y = .  So, you just have y.

Now substitute it into (1) and find x.