Question

Which points satisfy this linear-quadratic system of equations? x + y = 1 y = 4x − 3 − x2

Answer 1

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)