How do I solve x+y=1 and 5x-4y=-7?

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