Finding the point of interception?

Question

HOW (not what is) would I find the intercepting point of:

x^2+y=6
and
x+y=4

Answer 1

The intercept point must satisfy both equations. Thus change the second equation to:
y = 4 - x, and put it into the first one to get:
x^2 + 4 - x = 6,
or: x^2 - x - 2 = 0
factorize it to be:
(x - 2)(x + 1) = 0
thus x = 2 or x = -1.
The intercept points are therefore: (2, 2) and (-1, 5).