# Solve by Substitution y^2=x^2-64 , -3y=x+8

,
Solve for in the first equation.
Rewrite the equation as .
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.
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Combine the opposite terms in .
Subtract from .
Solve for in the first equation.
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to .
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 .
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^2=x^2-64 , -3y=x+8