Since we already know that y = 2x - 1, we can substitution method to solve the system. Substitute the expression 2x - 1 in place of y in the other equation.
4x - 7y = -23
4x - 7(2x - 1) = -23 iff
4x - 14x + 7 = -23 iff
-10x + 7 = -23 iff
-10x = -30 iff
x = 3
Now plug in x = 3 into any of the two equation to find y.
y = 2x - 1
y = 2(3) - 1 = 6 - 1 = 5
Thus the solution is (3, 5)