Solve the linear system using elimination

4x - y = 5     (1)

4x + 4y = -4    divide this equation through by 4 →   x + y  = -1   (2)

Add  (1) and (2)

5x  = 4      divide by 5 on both sides

x = 4/5  

And using (2) to find y, we have that

(4/5) + y = -1     subtract 4/5 from each side

y = -(1 + 4/5)  = -9/5