Solve the following system.
x²-y=3
x-y=-3
the solution set

Eliminate the y’s via elimination (subtract both of the equations):
x^2 - x = 6
x^2 - x - 6 = 0

Factor the quadratic:
(x - 3)(x + 2) = 0

Set each equation equal to 0 and solve.
x - 3 = 0 , x + 2 = 0
x = 3 , x = -2

Plug in the 1st value for x into the second equation:
3 - y = -3
-y = -6
y = 6

Plug in the second value for x into the second equation:
-2 - y = -3
-y = -1
y = 1

{(3,6)}
or
{(-2,1)}