# Solve by Addition/Elimination 4x^2-2y^2=-4 , 3x^2+5y^2=23

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Reorder the polynomial.
Reorder the polynomial.
Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
Simplify .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Multiply by .
Simplify .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Multiply by .
Add the two equations together to eliminate from the system.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Substitute the value found for into one of the original equations, then solve for .
Substitute the value found for into one of the original equations to solve for .
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 .
This is the final solution to the independent system of equations.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Any root of is .
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.
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.
The final result is the combination of all values of with all values of .
The result can be shown in multiple forms.
Point Form:
Equation Form:
Solve by Addition/Elimination 4x^2-2y^2=-4 , 3x^2+5y^2=23