,

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Divide by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Factor out of .

Factor out of .

Factor out of .

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.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Simplify .

Simplify each term.

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.

Apply the distributive property.

Multiply by .

Apply the distributive property.

Multiply by .

Multiply by .

Add and .

Solve for in the first equation.

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

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.

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.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Simplify .

Raise to the power of .

Add and .

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Simplify .

Raise to the power of .

Add and .

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

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.

Apply the distributive property.

Multiply by .

Apply the distributive property.

Multiply by .

Multiply by .

Add and .

Solve for in the first equation.

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

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.

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.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Simplify .

Raise to the power of .

Add and .

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Multiply by .

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Simplify .

Raise to the power of .

Add and .

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Multiply by .

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 2x^2-4y^2=-8 , 5x^2+3y^2=32