Solve the following systems of equations simultaneously (x-1)^2+y^2=32 . x+y=1

since y = 1-x, use that to get

(x-1)^2 + (1-x)^2 = 32
(x-1)^2 = 16
x-1 = ±4
x = -3 or 5
y = 4 or -4