# Solve by Substitution y^2+x^2=65 , y+x=7

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Subtract from both sides of the equation.
Replace all occurrences of with in each 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 .
Solve for in the first equation.
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 with in each equation.
Replace all occurrences of in with .
Simplify .
Multiply by .
Subtract from .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Multiply by .