y = 4x - 3 - x^2
now sub that in for y in the other equation
x + y = 1
x + 4x - 3 - x^2 = 1
-x^2 + 5x - 4 = 0
(-x + 1)(x - 4) = 0
-x + 1 = 0 y = 4x - 3 - x^2
-x = -1 y = 4(1) - 3 - 1^2
x = 1 y = 4 - 3 - 1 = 0
x - 4 = 0 y = 4x - 3 - x^2
x = 4 y = 4(4) - 3 - 4^2
y = 16 - 3 - 16
y = -3
points that satisfy this are : (1,0) and (4,-3)