,

Subtract from both sides of the equation.

Replace all occurrences of in with .

Simplify .

Simplify each term.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Move .

Multiply by .

Multiply by .

Multiply by .

Subtract from .

Add and .

Subtract from both sides of the equation.

Subtract from .

Factor the left side of the equation.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Let . Substitute for all occurrences of .

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.

Factor.

Replace all occurrences of with .

Remove unnecessary parentheses.

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

Set equal to and solve for .

Set equal to .

Add to both sides of the equation.

Set equal to and solve for .

Set equal to .

Subtract from both sides of the equation.

The final solution is all the values that make true.

Replace all occurrences of in with .

Simplify .

Multiply by .

Subtract from .

Replace all occurrences of in with .

Simplify .

Multiply by .

Add and .

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^2+x^2=65 , y+x=7