So with this type of question, you are expected to solve the systems of equations simultaneously
Let 4x + 4y = -12 ..... (1)
3x - 4y = -23 ..... (2)
By summing (2) and (1)
⇒ 4x + 3x + 4y + (-4y) = -12 + (-23)
7x = -35
⇒ 7x ÷ 7 = -35 ÷ 7
⇒ x = - 5
By substituting x into (1)
If 4x + 4y = -12 ..... (1)
then 4 (-5) + 4y = -12
⇒ 4y = -12 + 20
⇒ y = 8 ÷ 4
⇒ y = 2
∴ the solution for the system of equation are x = - 5 ; y = 2