Answer :

Use substitution method:

x + y = 1 --> y = x - 1 (then plug in to other equation)
5x - 4y = -7 --> 5x - 4(x - 1) = -7 -->
5x -4x + 4 = -7 --> x = -11 (then plug into one of original equations to find y)

x + y = 1 --> (-11) + y = 1 --> y = 12