# Solve by Substitution x^2+y^2=1 , x^2-y^2=1

,
Solve for in the first equation.
Add to both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Solve the system .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Solve for in the first equation.
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Raising to any positive power yields .
Any root of is .
Solve the system .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply by .
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Solve for in the first equation.
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Raising to any positive power yields .