Find the Points of Intersection x^2+y^2=12 , y^2-2x^2=6

$x^{2} + y^{2} = 12$ , $y^{2} - 2 x^{2} = 6$

Solve for $x$ in $x^{2} + y^{2} = 12$ .

Subtract $y^{2}$ from both sides of the equation.

$x^{2} = 12 - y^{2}$

$y^{2} - 2 x^{2} = 6$

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

$x = \pm \sqrt{12 - y^{2}}$

$y^{2} - 2 x^{2} = 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{12 - y^{2}}$

$y^{2} - 2 x^{2} = 6$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{12 - y^{2}}$

$y^{2} - 2 x^{2} = 6$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{12 - y^{2}}$

$x = - \sqrt{12 - y^{2}}$

$y^{2} - 2 x^{2} = 6$

$x = \sqrt{12 - y^{2}}$

$x = - \sqrt{12 - y^{2}}$

$y^{2} - 2 x^{2} = 6$

$x = \sqrt{12 - y^{2}}$

$x = - \sqrt{12 - y^{2}}$

$y^{2} - 2 x^{2} = 6$

Solve the system $x = \sqrt{12 - y^{2}}, y^{2} - 2 x^{2} = 6$ .

Replace all occurrences of $x$ with $\sqrt{12 - y^{2}}$ in each equation.

Replace all occurrences of $x$ in $y^{2} - 2 x^{2} = 6$ with $\sqrt{12 - y^{2}}$ .

$y^{2} - 2 {(\sqrt{12 - y^{2}})}^{2} = 6$

$x = \sqrt{12 - y^{2}}$

Simplify the left side.

Simplify $y^{2} - 2 {(\sqrt{12 - y^{2}})}^{2}$ .

Simplify each term.

Rewrite ${\sqrt{12 - y^{2}}}^{2}$ as $12 - y^{2}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{12 - y^{2}}$ as ${(12 - y^{2})}^{\frac{1}{2}}$ .

$y^{2} - 2 {({(12 - y^{2})}^{\frac{1}{2}})}^{2} = 6$

$x = \sqrt{12 - y^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y^{2} - 2 {(12 - y^{2})}^{\frac{1}{2} \cdot 2} = 6$

$x = \sqrt{12 - y^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$y^{2} - 2 {(12 - y^{2})}^{\frac{2}{2}} = 6$

$x = \sqrt{12 - y^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y^{2} - 2 {(12 - y^{2})}^{\frac{2}{2}} = 6$

$x = \sqrt{12 - y^{2}}$

Rewrite the expression.

$y^{2} - 2 (12 - y^{2}) = 6$

$x = \sqrt{12 - y^{2}}$

$y^{2} - 2 (12 - y^{2}) = 6$

$x = \sqrt{12 - y^{2}}$

Simplify.

$y^{2} - 2 (12 - y^{2}) = 6$

$x = \sqrt{12 - y^{2}}$

$y^{2} - 2 (12 - y^{2}) = 6$

$x = \sqrt{12 - y^{2}}$

Apply the distributive property.

$y^{2} - 2 \cdot 12 - 2 (- y^{2}) = 6$

$x = \sqrt{12 - y^{2}}$

Multiply $- 2$ by $12$ .

$y^{2} - 24 - 2 (- y^{2}) = 6$

$x = \sqrt{12 - y^{2}}$

Multiply $- 1$ by $- 2$ .

$y^{2} - 24 + 2 y^{2} = 6$

$x = \sqrt{12 - y^{2}}$

$y^{2} - 24 + 2 y^{2} = 6$

$x = \sqrt{12 - y^{2}}$

Add $y^{2}$ and $2 y^{2}$ .

$3 y^{2} - 24 = 6$

$x = \sqrt{12 - y^{2}}$

$3 y^{2} - 24 = 6$

$x = \sqrt{12 - y^{2}}$

$3 y^{2} - 24 = 6$

$x = \sqrt{12 - y^{2}}$

$3 y^{2} - 24 = 6$

$x = \sqrt{12 - y^{2}}$

Solve for $y$ in $3 y^{2} - 24 = 6$ .

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

Add $24$ to both sides of the equation.

$3 y^{2} = 6 + 24$

$x = \sqrt{12 - y^{2}}$

Add $6$ and $24$ .

$3 y^{2} = 30$

$x = \sqrt{12 - y^{2}}$

$3 y^{2} = 30$

$x = \sqrt{12 - y^{2}}$

Divide each term in $3 y^{2} = 30$ by $3$ and simplify.

Divide each term in $3 y^{2} = 30$ by $3$ .

$\frac{3 y^{2}}{3} = \frac{30}{3}$

$x = \sqrt{12 - y^{2}}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y^{2}}{3} = \frac{30}{3}$

$x = \sqrt{12 - y^{2}}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{30}{3}$

$x = \sqrt{12 - y^{2}}$

$y^{2} = \frac{30}{3}$

$x = \sqrt{12 - y^{2}}$

$y^{2} = \frac{30}{3}$

$x = \sqrt{12 - y^{2}}$

Simplify the right side.

Divide $30$ by $3$ .

$y^{2} = 10$

$x = \sqrt{12 - y^{2}}$

$y^{2} = 10$

$x = \sqrt{12 - y^{2}}$

$y^{2} = 10$

$x = \sqrt{12 - y^{2}}$

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

$y = \pm \sqrt{10}$

$x = \sqrt{12 - y^{2}}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{10}$

$x = \sqrt{12 - y^{2}}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{10}$

$x = \sqrt{12 - y^{2}}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{10}, - \sqrt{10}$

$x = \sqrt{12 - y^{2}}$

$y = \sqrt{10}, - \sqrt{10}$

$x = \sqrt{12 - y^{2}}$

$y = \sqrt{10}, - \sqrt{10}$

$x = \sqrt{12 - y^{2}}$

Replace all occurrences of $y$ with $\sqrt{10}$ in each equation.

Replace all occurrences of $y$ in $x = \sqrt{12 - y^{2}}$ with $\sqrt{10}$ .

$x = \sqrt{12 - {(\sqrt{10})}^{2}}$

$y = \sqrt{10}$

Simplify the right side.

Simplify $\sqrt{12 - {(\sqrt{10})}^{2}}$ .

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$x = \sqrt{12 - {(10^{\frac{1}{2}})}^{2}}$

$y = \sqrt{10}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \sqrt{12 - 10^{\frac{1}{2} \cdot 2}}$

$y = \sqrt{10}$

Combine $\frac{1}{2}$ and $2$ .

$x = \sqrt{12 - 10^{\frac{2}{2}}}$

$y = \sqrt{10}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \sqrt{12 - 10^{\frac{2}{2}}}$

$y = \sqrt{10}$

Rewrite the expression.

$x = \sqrt{12 - 10}$

$y = \sqrt{10}$

$x = \sqrt{12 - 10}$

$y = \sqrt{10}$

Evaluate the exponent.

$x = \sqrt{12 - 1 \cdot 10}$

$y = \sqrt{10}$

$x = \sqrt{12 - 1 \cdot 10}$

$y = \sqrt{10}$

Simplify the expression.

Multiply $- 1$ by $10$ .

$x = \sqrt{12 - 10}$

$y = \sqrt{10}$

Subtract $10$ from $12$ .

$x = \sqrt{2}$

$y = \sqrt{10}$

$x = \sqrt{2}$

$y = \sqrt{10}$

$x = \sqrt{2}$

$y = \sqrt{10}$

$x = \sqrt{2}$

$y = \sqrt{10}$

$x = \sqrt{2}$

$y = \sqrt{10}$

Replace all occurrences of $y$ with $- \sqrt{10}$ in each equation.

Replace all occurrences of $y$ in $x = \sqrt{12 - y^{2}}$ with $- \sqrt{10}$ .

$x = \sqrt{12 - {(- \sqrt{10})}^{2}}$

$y = - \sqrt{10}$

Simplify the right side.

Simplify $\sqrt{12 - {(- \sqrt{10})}^{2}}$ .

Apply the product rule to $- \sqrt{10}$ .

$x = \sqrt{12 - ({(- 1)}^{2} {\sqrt{10}}^{2})}$

$y = - \sqrt{10}$

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Move ${(- 1)}^{2}$ .

$x = \sqrt{12 + {(- 1)}^{2} \cdot (- 1 {\sqrt{10}}^{2})}$

$y = - \sqrt{10}$

Multiply ${(- 1)}^{2}$ by $- 1$ .

Raise $- 1$ to the power of $1$ .

$x = \sqrt{12 + {(- 1)}^{2} \cdot ((- 1) {\sqrt{10}}^{2})}$

$y = - \sqrt{10}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \sqrt{12 + {(- 1)}^{2 + 1} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

$x = \sqrt{12 + {(- 1)}^{2 + 1} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

Add $2$ and $1$ .

$x = \sqrt{12 + {(- 1)}^{3} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

$x = \sqrt{12 + {(- 1)}^{3} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

Raise $- 1$ to the power of $3$ .

$x = \sqrt{12 - {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$x = \sqrt{12 - {(10^{\frac{1}{2}})}^{2}}$

$y = - \sqrt{10}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \sqrt{12 - 10^{\frac{1}{2} \cdot 2}}$

$y = - \sqrt{10}$

Combine $\frac{1}{2}$ and $2$ .

$x = \sqrt{12 - 10^{\frac{2}{2}}}$

$y = - \sqrt{10}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \sqrt{12 - 10^{\frac{2}{2}}}$

$y = - \sqrt{10}$

Rewrite the expression.

$x = \sqrt{12 - 10}$

$y = - \sqrt{10}$

$x = \sqrt{12 - 10}$

$y = - \sqrt{10}$

Evaluate the exponent.

$x = \sqrt{12 - 1 \cdot 10}$

$y = - \sqrt{10}$

$x = \sqrt{12 - 1 \cdot 10}$

$y = - \sqrt{10}$

Simplify the expression.

Multiply $- 1$ by $10$ .

$x = \sqrt{12 - 10}$

$y = - \sqrt{10}$

Subtract $10$ from $12$ .

$x = \sqrt{2}$

$y = - \sqrt{10}$

$x = \sqrt{2}$

$y = - \sqrt{10}$

$x = \sqrt{2}$

$y = - \sqrt{10}$

$x = \sqrt{2}$

$y = - \sqrt{10}$

$x = \sqrt{2}$

$y = - \sqrt{10}$

$x = \sqrt{2}$

$y = - \sqrt{10}$

Solve the system $x = - \sqrt{12 - y^{2}}, y^{2} - 2 x^{2} = 6$ .

Replace all occurrences of $x$ with $- \sqrt{12 - y^{2}}$ in each equation.

Replace all occurrences of $x$ in $y^{2} - 2 x^{2} = 6$ with $- \sqrt{12 - y^{2}}$ .

$y^{2} - 2 {(- \sqrt{12 - y^{2}})}^{2} = 6$

$x = - \sqrt{12 - y^{2}}$

Simplify the left side.

Simplify $y^{2} - 2 {(- \sqrt{12 - y^{2}})}^{2}$ .

Simplify each term.

Apply the product rule to $- \sqrt{12 - y^{2}}$ .

$y^{2} - 2 ({(- 1)}^{2} {\sqrt{12 - y^{2}}}^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

Raise $- 1$ to the power of $2$ .

$y^{2} - 2 (1 {\sqrt{12 - y^{2}}}^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

Multiply ${\sqrt{12 - y^{2}}}^{2}$ by $1$ .

$y^{2} - 2 {\sqrt{12 - y^{2}}}^{2} = 6$

$x = - \sqrt{12 - y^{2}}$

Rewrite ${\sqrt{12 - y^{2}}}^{2}$ as $12 - y^{2}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{12 - y^{2}}$ as ${(12 - y^{2})}^{\frac{1}{2}}$ .

$y^{2} - 2 {({(12 - y^{2})}^{\frac{1}{2}})}^{2} = 6$

$x = - \sqrt{12 - y^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y^{2} - 2 {(12 - y^{2})}^{\frac{1}{2} \cdot 2} = 6$

$x = - \sqrt{12 - y^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$y^{2} - 2 {(12 - y^{2})}^{\frac{2}{2}} = 6$

$x = - \sqrt{12 - y^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y^{2} - 2 {(12 - y^{2})}^{\frac{2}{2}} = 6$

$x = - \sqrt{12 - y^{2}}$

Rewrite the expression.

$y^{2} - 2 (12 - y^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

$y^{2} - 2 (12 - y^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

Simplify.

$y^{2} - 2 (12 - y^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

$y^{2} - 2 (12 - y^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

Apply the distributive property.

$y^{2} - 2 \cdot 12 - 2 (- y^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

Multiply $- 2$ by $12$ .

$y^{2} - 24 - 2 (- y^{2}) = 6$

$x = - \sqrt{12 - y^{2}}$

Multiply $- 1$ by $- 2$ .

$y^{2} - 24 + 2 y^{2} = 6$

$x = - \sqrt{12 - y^{2}}$

$y^{2} - 24 + 2 y^{2} = 6$

$x = - \sqrt{12 - y^{2}}$

Add $y^{2}$ and $2 y^{2}$ .

$3 y^{2} - 24 = 6$

$x = - \sqrt{12 - y^{2}}$

$3 y^{2} - 24 = 6$

$x = - \sqrt{12 - y^{2}}$

$3 y^{2} - 24 = 6$

$x = - \sqrt{12 - y^{2}}$

$3 y^{2} - 24 = 6$

$x = - \sqrt{12 - y^{2}}$

Solve for $y$ in $3 y^{2} - 24 = 6$ .

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

Add $24$ to both sides of the equation.

$3 y^{2} = 6 + 24$

$x = - \sqrt{12 - y^{2}}$

Add $6$ and $24$ .

$3 y^{2} = 30$

$x = - \sqrt{12 - y^{2}}$

$3 y^{2} = 30$

$x = - \sqrt{12 - y^{2}}$

Divide each term in $3 y^{2} = 30$ by $3$ and simplify.

Divide each term in $3 y^{2} = 30$ by $3$ .

$\frac{3 y^{2}}{3} = \frac{30}{3}$

$x = - \sqrt{12 - y^{2}}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y^{2}}{3} = \frac{30}{3}$

$x = - \sqrt{12 - y^{2}}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{30}{3}$

$x = - \sqrt{12 - y^{2}}$

$y^{2} = \frac{30}{3}$

$x = - \sqrt{12 - y^{2}}$

$y^{2} = \frac{30}{3}$

$x = - \sqrt{12 - y^{2}}$

Simplify the right side.

Divide $30$ by $3$ .

$y^{2} = 10$

$x = - \sqrt{12 - y^{2}}$

$y^{2} = 10$

$x = - \sqrt{12 - y^{2}}$

$y^{2} = 10$

$x = - \sqrt{12 - y^{2}}$

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

$y = \pm \sqrt{10}$

$x = - \sqrt{12 - y^{2}}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{10}$

$x = - \sqrt{12 - y^{2}}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{10}$

$x = - \sqrt{12 - y^{2}}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{10}, - \sqrt{10}$

$x = - \sqrt{12 - y^{2}}$

$y = \sqrt{10}, - \sqrt{10}$

$x = - \sqrt{12 - y^{2}}$

$y = \sqrt{10}, - \sqrt{10}$

$x = - \sqrt{12 - y^{2}}$

Replace all occurrences of $y$ with $\sqrt{10}$ in each equation.

Replace all occurrences of $y$ in $x = - \sqrt{12 - y^{2}}$ with $\sqrt{10}$ .

$x = - \sqrt{12 - {(\sqrt{10})}^{2}}$

$y = \sqrt{10}$

Simplify the right side.

Simplify $- \sqrt{12 - {(\sqrt{10})}^{2}}$ .

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$x = - \sqrt{12 - {(10^{\frac{1}{2}})}^{2}}$

$y = \sqrt{10}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = - \sqrt{12 - 10^{\frac{1}{2} \cdot 2}}$

$y = \sqrt{10}$

Combine $\frac{1}{2}$ and $2$ .

$x = - \sqrt{12 - 10^{\frac{2}{2}}}$

$y = \sqrt{10}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = - \sqrt{12 - 10^{\frac{2}{2}}}$

$y = \sqrt{10}$

Rewrite the expression.

$x = - \sqrt{12 - 10}$

$y = \sqrt{10}$

$x = - \sqrt{12 - 10}$

$y = \sqrt{10}$

Evaluate the exponent.

$x = - \sqrt{12 - 1 \cdot 10}$

$y = \sqrt{10}$

$x = - \sqrt{12 - 1 \cdot 10}$

$y = \sqrt{10}$

Simplify the expression.

Multiply $- 1$ by $10$ .

$x = - \sqrt{12 - 10}$

$y = \sqrt{10}$

Subtract $10$ from $12$ .

$x = - \sqrt{2}$

$y = \sqrt{10}$

$x = - \sqrt{2}$

$y = \sqrt{10}$

$x = - \sqrt{2}$

$y = \sqrt{10}$

$x = - \sqrt{2}$

$y = \sqrt{10}$

$x = - \sqrt{2}$

$y = \sqrt{10}$

Replace all occurrences of $y$ with $- \sqrt{10}$ in each equation.

Replace all occurrences of $y$ in $x = - \sqrt{12 - y^{2}}$ with $- \sqrt{10}$ .

$x = - \sqrt{12 - {(- \sqrt{10})}^{2}}$

$y = - \sqrt{10}$

Simplify the right side.

Simplify $- \sqrt{12 - {(- \sqrt{10})}^{2}}$ .

Apply the product rule to $- \sqrt{10}$ .

$x = - \sqrt{12 - ({(- 1)}^{2} {\sqrt{10}}^{2})}$

$y = - \sqrt{10}$

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Move ${(- 1)}^{2}$ .

$x = - \sqrt{12 + {(- 1)}^{2} \cdot (- 1 {\sqrt{10}}^{2})}$

$y = - \sqrt{10}$

Multiply ${(- 1)}^{2}$ by $- 1$ .

Raise $- 1$ to the power of $1$ .

$x = - \sqrt{12 + {(- 1)}^{2} \cdot ((- 1) {\sqrt{10}}^{2})}$

$y = - \sqrt{10}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - \sqrt{12 + {(- 1)}^{2 + 1} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

$x = - \sqrt{12 + {(- 1)}^{2 + 1} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

Add $2$ and $1$ .

$x = - \sqrt{12 + {(- 1)}^{3} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

$x = - \sqrt{12 + {(- 1)}^{3} {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

Raise $- 1$ to the power of $3$ .

$x = - \sqrt{12 - {\sqrt{10}}^{2}}$

$y = - \sqrt{10}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$x = - \sqrt{12 - {(10^{\frac{1}{2}})}^{2}}$

$y = - \sqrt{10}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = - \sqrt{12 - 10^{\frac{1}{2} \cdot 2}}$

$y = - \sqrt{10}$

Combine $\frac{1}{2}$ and $2$ .

$x = - \sqrt{12 - 10^{\frac{2}{2}}}$

$y = - \sqrt{10}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = - \sqrt{12 - 10^{\frac{2}{2}}}$

$y = - \sqrt{10}$

Rewrite the expression.

$x = - \sqrt{12 - 10}$

$y = - \sqrt{10}$

$x = - \sqrt{12 - 10}$

$y = - \sqrt{10}$

Evaluate the exponent.

$x = - \sqrt{12 - 1 \cdot 10}$

$y = - \sqrt{10}$

$x = - \sqrt{12 - 1 \cdot 10}$

$y = - \sqrt{10}$

Simplify the expression.

Multiply $- 1$ by $10$ .

$x = - \sqrt{12 - 10}$

$y = - \sqrt{10}$

Subtract $10$ from $12$ .

$x = - \sqrt{2}$

$y = - \sqrt{10}$

$x = - \sqrt{2}$

$y = - \sqrt{10}$

$x = - \sqrt{2}$

$y = - \sqrt{10}$

$x = - \sqrt{2}$

$y = - \sqrt{10}$

$x = - \sqrt{2}$

$y = - \sqrt{10}$

$x = - \sqrt{2}$

$y = - \sqrt{10}$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\sqrt{2}, \sqrt{10})$

$(\sqrt{2}, - \sqrt{10})$

$(- \sqrt{2}, \sqrt{10})$

$(- \sqrt{2}, - \sqrt{10})$

The result can be shown in multiple forms.

Point Form:

$(\sqrt{2}, \sqrt{10}), (\sqrt{2}, - \sqrt{10}), (- \sqrt{2}, \sqrt{10}), (- \sqrt{2}, - \sqrt{10})$

Equation Form:

$x = \sqrt{2}, y = \sqrt{10}$

$x = \sqrt{2}, y = - \sqrt{10}$

$x = - \sqrt{2}, y = \sqrt{10}$

$x = - \sqrt{2}, y = - \sqrt{10}$

Find the Points of Intersection x^2+y^2=12 , y^2-2x^2=6

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