Since the first equation gives you an expression for y, it is convenient to use that in the second equation. Since the second equation has a factor of 3 that can be removed from all terms, it may make the math easier to do that.
Revised 2nd equation:
.. x -y = 1
Substituting for y:
.. x -(2x +4) = 1 . . . . . use the expressiion for y in place of y
.. -x -4 = 1 . . . . . . . . . simplify
.. -4 = 1 +x . . . . . . . . . add x
.. -5 = x . . . . . . . . . . . subtract 1
y = 2x +4
.. = 2(-5) +4
.. = -6
The solution is (x, y) = (-5, -6).