Solve the following system.

x 2 - y = 3

x - y = - 3

The solution set

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.