I think you are missing an x in the equation -3 - 4y= - 23.
If not, then multiply -3x + y = 2 by 4. This will eliminate y.
4(-3x + y) = 4(2)
-12x + 4y = 8
-3 - 4y = - 23
Do you see that 4y and -4y disappear?
-15x = -15
x = -15/-15
x = 1
Can you find y?