# Solve the System of Equations 2x^2+3y^2=19 2x^2+y^2=9

Solve the System of Equations 2x^2+3y^2=19 2x^2+y^2=9
Solve for in .
Subtract from 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 the left side.
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 .
Multiply by .
Subtract from .
Solve for in .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Divide by .
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.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
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.
Evaluate the exponent.
Simplify the expression.
Multiply by .
Subtract from .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify the expression.
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.
Evaluate the exponent.
Simplify the expression.
Multiply by .
Subtract from .
Solve the system .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the left side.
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 .
Multiply by .
Subtract from .
Solve for in .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Divide by .
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.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
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.
Evaluate the exponent.
Simplify the expression.
Multiply by .
Subtract from .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify the expression.
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.
Evaluate the exponent.
Simplify the expression.
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:
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