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

Answer:

{ (3,6) }

or

{ (-2,1) }