x = 3 - y^2

Question

y = x - 3

Find the points of intersection.

If someone could even get me to the point where it gets written in general form (both equations set to 0..) I would be forever grateful.

Answer 1

sub the second equation into the first, so

x = 3 - (x-3)^2
x = 3 - (x^2 - 6x + 9)
x^2 - 5x + 6 = 0
(x-2)(x-3) = 0
x = 2 or x = 3

if x = 2, then y = 2-3 = -1
if x = 3, then y = 3-3 = 0

so they intersect at (2,-1) and (3,0)