,

Replace with in the equation.

Solve the equation for .

Subtract from both sides of the equation.

Move to the left side of the equation by adding it to both sides.

Add and .

Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to and solve.

Set the first factor equal to .

Add to both sides of the equation.

Set the next factor equal to and solve.

Set the next factor equal to .

Subtract from both sides of the equation.

The final solution is all the values that make true.

Replace with in the equation.

Simplify .

Multiply by .

Subtract from .

Replace with in the equation.

Simplify .

Multiply by .

Subtract from .

The solution to the system is the complete set of ordered pairs that are valid solutions.

The result can be shown in multiple forms.

Point Form:

Equation Form:

Solve by Substitution y=x^2-5 , y=2x-2