# Solve by Substitution 4x^2-3y^2=-11 , 5x^2+2y^2=38

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Solve for in the first equation.
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 .
Move the negative in front of the fraction.
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.
Combine the numerators over the common denominator.
Rewrite as .
Factor the perfect power out of .
Factor the perfect power out of .
Rearrange the fraction .
Pull terms out from under the radical.
Combine and .
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 .
Simplify each term.
Apply the product rule to .
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.
Raise to the power of .
Combine and .
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Multiply by .
Multiply by .
Simplify with factoring out.
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Solve for in the first equation.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply.
Multiply by .
Multiply by .
Multiply by .
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.
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 the numerator.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Divide by .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify the numerator.
Raise to the power of .
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Divide by .
Solve the system .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Use the power rule to distribute the exponent.
Apply the product rule to .
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.
Raise to the power of .
Combine and .
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Multiply by .
Multiply by .
Simplify with factoring out.
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Solve for in the first equation.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply.
Multiply by .
Multiply by .
Multiply by .
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.
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 the numerator.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the expression.
Divide by .
Multiply by .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify the numerator.
Raise to the power of .
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the expression.
Divide by .
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 4x^2-3y^2=-11 , 5x^2+2y^2=38