Question

Solve the following system.

x 2 - y = 3
x - y = -3

The solution set

Answer 1

One approach is to isolate y in the bottom formula, then fill it in to the top one:

x-y=-3 => y = 3+x

so substitute 3+x for y in the top formula (watch the signs) and simplify

x² - 3 - x = 3 => x² -x -6 = 0 => (x+2)(x-3)=0

so x=-2 or x=3.

for x=-2, y=1
for x=3, y=6

These are the solutions.