Solve by Substitution 2x^2-5y^2=-12 , 5x^2+2y^2=28

$2 x^{2} - 5 y^{2} = - 12$ , $5 x^{2} + 2 y^{2} = 28$

Step 1

Solve for $x$ in $2 x^{2} - 5 y^{2} = - 12$ .

Add $5 y^{2}$ to both sides of the equation.

$2 x^{2} = - 12 + 5 y^{2}$

$5 x^{2} + 2 y^{2} = 28$

Divide each term in $2 x^{2} = - 12 + 5 y^{2}$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 12 + 5 y^{2}$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 12}{2} + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 12}{2} + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

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

$x^{2} = \frac{- 12}{2} + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x^{2} = \frac{- 12}{2} + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x^{2} = \frac{- 12}{2} + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

Simplify the right side.

Divide $- 12$ by $2$ .

$x^{2} = - 6 + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x^{2} = - 6 + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x^{2} = - 6 + \frac{5 y^{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

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

$x = \pm \sqrt{- 6 + \frac{5 y^{2}}{2}}$

$5 x^{2} + 2 y^{2} = 28$

Simplify $\pm \sqrt{- 6 + \frac{5 y^{2}}{2}}$ .

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \pm \sqrt{- 6 \cdot \frac{2}{2} + \frac{5 y^{2}}{2}}$

$5 x^{2} + 2 y^{2} = 28$

Combine $- 6$ and $\frac{2}{2}$ .

$x = \pm \sqrt{\frac{- 6 \cdot 2}{2} + \frac{5 y^{2}}{2}}$

$5 x^{2} + 2 y^{2} = 28$

Combine the numerators over the common denominator.

$x = \pm \sqrt{\frac{- 6 \cdot 2 + 5 y^{2}}{2}}$

$5 x^{2} + 2 y^{2} = 28$

Multiply $- 6$ by $2$ .

$x = \pm \sqrt{\frac{- 12 + 5 y^{2}}{2}}$

$5 x^{2} + 2 y^{2} = 28$

Rewrite $\sqrt{\frac{- 12 + 5 y^{2}}{2}}$ as $\frac{\sqrt{- 12 + 5 y^{2}}}{\sqrt{2}}$ .

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}}}{\sqrt{2}}$

$5 x^{2} + 2 y^{2} = 28$

Multiply $\frac{\sqrt{- 12 + 5 y^{2}}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

$5 x^{2} + 2 y^{2} = 28$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{- 12 + 5 y^{2}}}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

$5 x^{2} + 2 y^{2} = 28$

Raise $\sqrt{2}$ to the power of $1$ .

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

$5 x^{2} + 2 y^{2} = 28$

Raise $\sqrt{2}$ to the power of $1$ .

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{\sqrt{2} \sqrt{2}}$

$5 x^{2} + 2 y^{2} = 28$

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

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

$5 x^{2} + 2 y^{2} = 28$

Add $1$ and $1$ .

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{{\sqrt{2}}^{2}}$

$5 x^{2} + 2 y^{2} = 28$

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

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

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

$5 x^{2} + 2 y^{2} = 28$

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

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

$5 x^{2} + 2 y^{2} = 28$

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

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2^{\frac{2}{2}}}$

$5 x^{2} + 2 y^{2} = 28$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2^{\frac{2}{2}}}$

$5 x^{2} + 2 y^{2} = 28$

Rewrite the expression.

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

Evaluate the exponent.

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x = \pm \frac{\sqrt{- 12 + 5 y^{2}} \sqrt{2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

Combine using the product rule for radicals.

$x = \pm \frac{\sqrt{(- 12 + 5 y^{2}) \cdot 2}}{2}$

$5 x^{2} + 2 y^{2} = 28$

Reorder factors in $\pm \frac{\sqrt{(- 12 + 5 y^{2}) \cdot 2}}{2}$ .

$x = \pm \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x = \pm \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 x^{2} + 2 y^{2} = 28$

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.

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 x^{2} + 2 y^{2} = 28$

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

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 x^{2} + 2 y^{2} = 28$

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

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 x^{2} + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 x^{2} + 2 y^{2} = 28$

Step 2

Solve the system $x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}, 5 x^{2} + 2 y^{2} = 28$ .

Replace all occurrences of $x$ with $\frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ in each equation.

Replace all occurrences of $x$ in $5 x^{2} + 2 y^{2} = 28$ with $\frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ .

$5 {(\frac{\sqrt{2 (- 12 + 5 y^{2})}}{2})}^{2} + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the left side.

Simplify $5 {(\frac{\sqrt{2 (- 12 + 5 y^{2})}}{2})}^{2} + 2 y^{2}$ .

Simplify each term.

Apply the product rule to $\frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ .

$5 (\frac{{\sqrt{2 (- 12 + 5 y^{2})}}^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the numerator.

Rewrite ${\sqrt{2 (- 12 + 5 y^{2})}}^{2}$ as $2 (- 12 + 5 y^{2})$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 (- 12 + 5 y^{2})}$ as ${(2 (- 12 + 5 y^{2}))}^{\frac{1}{2}}$ .

$5 (\frac{{({(2 (- 12 + 5 y^{2}))}^{\frac{1}{2}})}^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$5 (\frac{{(2 (- 12 + 5 y^{2}))}^{\frac{1}{2} \cdot 2}}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$5 (\frac{{(2 (- 12 + 5 y^{2}))}^{\frac{2}{2}}}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$5 (\frac{{(2 (- 12 + 5 y^{2}))}^{\frac{2}{2}}}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Rewrite the expression.

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify.

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Apply the distributive property.

$5 (\frac{2 \cdot - 12 + 2 (5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $2$ by $- 12$ .

$5 (\frac{- 24 + 2 (5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $5$ by $2$ .

$5 (\frac{- 24 + 10 y^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $- 24 + 10 y^{2}$ .

Factor $2$ out of $- 24$ .

$5 (\frac{2 (- 12) + 10 y^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $10 y^{2}$ .

$5 (\frac{2 (- 12) + 2 (5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $2 (- 12) + 2 (5 y^{2})$ .

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$5 (\frac{2 (- 12 + 5 y^{2})}{4}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$5 (\frac{2 (- 12 + 5 y^{2})}{2 \cdot 2}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factor.

$5 (\frac{2 (- 12 + 5 y^{2})}{2 \cdot 2}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Rewrite the expression.

$5 (\frac{- 12 + 5 y^{2}}{2}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{- 12 + 5 y^{2}}{2}) + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Combine $5$ and $\frac{- 12 + 5 y^{2}}{2}$ .

$\frac{5 (- 12 + 5 y^{2})}{2} + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$\frac{5 (- 12 + 5 y^{2})}{2} + 2 y^{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

To write $2 y^{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 (- 12 + 5 y^{2})}{2} + 2 y^{2} \cdot \frac{2}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify terms.

Combine $2 y^{2}$ and $\frac{2}{2}$ .

$\frac{5 (- 12 + 5 y^{2})}{2} + \frac{2 y^{2} \cdot 2}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Combine the numerators over the common denominator.

$\frac{5 (- 12 + 5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$\frac{5 (- 12 + 5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 \cdot - 12 + 5 (5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $5$ by $- 12$ .

$\frac{- 60 + 5 (5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $5$ by $5$ .

$\frac{- 60 + 25 y^{2} + 2 y^{2} \cdot 2}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $2$ by $2$ .

$\frac{- 60 + 25 y^{2} + 4 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Add $25 y^{2}$ and $4 y^{2}$ .

$\frac{- 60 + 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$\frac{- 60 + 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify with factoring out.

Rewrite $- 60$ as $- 1 (60)$ .

$\frac{- 1 \cdot 60 + 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $- 1$ out of $29 y^{2}$ .

$\frac{- 1 \cdot 60 - (- 29 y^{2})}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $- 1$ out of $- 1 (60) - (- 29 y^{2})$ .

$\frac{- 1 (60 - 29 y^{2})}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Move the negative in front of the fraction.

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Solve for $y$ in $- \frac{60 - 29 y^{2}}{2} = 28$ .

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{60 - 29 y^{2}}{2}) = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{60 - 29 y^{2}}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{60 - 29 y^{2}}{2}$ into the numerator.

$- 2 \frac{- (60 - 29 y^{2})}{2} = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- (60 - 29 y^{2})}{2}) = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factor.

$2 \cdot (- 1 \frac{- (60 - 29 y^{2})}{2}) = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Rewrite the expression.

$60 - 29 y^{2} = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (60 - 29 y^{2}) = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $60 - 29 y^{2}$ by $1$ .

$60 - 29 y^{2} = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the right side.

Multiply $- 2$ by $28$ .

$60 - 29 y^{2} = - 56$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 56$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 56$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

Subtract $60$ from both sides of the equation.

$- 29 y^{2} = - 56 - 60$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Subtract $60$ from $- 56$ .

$- 29 y^{2} = - 116$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- 29 y^{2} = - 116$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Divide each term in $- 29 y^{2} = - 116$ by $- 29$ and simplify.

Divide each term in $- 29 y^{2} = - 116$ by $- 29$ .

$\frac{- 29 y^{2}}{- 29} = \frac{- 116}{- 29}$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the left side.

Cancel the common factor of $- 29$ .

Cancel the common factor.

$\frac{- 29 y^{2}}{- 29} = \frac{- 116}{- 29}$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y^{2} = \frac{- 116}{- 29}$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = \frac{- 116}{- 29}$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = \frac{- 116}{- 29}$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the right side.

Divide $- 116$ by $- 29$ .

$y^{2} = 4$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = 4$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = 4$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = \pm \sqrt{4}$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$y = \pm \sqrt{2^{2}}$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = \pm 2$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y = \pm 2$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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.

$y = 2$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = - 2$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = 2, - 2$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y = 2, - 2$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y = 2, - 2$

$x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ with $2$ .

$x = \frac{\sqrt{2 (- 12 + 5 {(2)}^{2})}}{2}$

$y = 2$

Simplify the right side.

Simplify $\frac{\sqrt{2 (- 12 + 5 {(2)}^{2})}}{2}$ .

Simplify the numerator.

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

$x = \frac{\sqrt{2 (- 12 + 5 \cdot 4)}}{2}$

$y = 2$

Multiply $5$ by $4$ .

$x = \frac{\sqrt{2 (- 12 + 20)}}{2}$

$y = 2$

Add $- 12$ and $20$ .

$x = \frac{\sqrt{2 \cdot 8}}{2}$

$y = 2$

Multiply $2$ by $8$ .

$x = \frac{\sqrt{16}}{2}$

$y = 2$

Rewrite $16$ as $4^{2}$ .

$x = \frac{\sqrt{4^{2}}}{2}$

$y = 2$

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

$x = \frac{4}{2}$

$y = 2$

$x = \frac{4}{2}$

$y = 2$

Divide $4$ by $2$ .

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

Replace all occurrences of $y$ with $- 2$ in each equation.

Replace all occurrences of $y$ in $x = \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ with $- 2$ .

$x = \frac{\sqrt{2 (- 12 + 5 {(- 2)}^{2})}}{2}$

$y = - 2$

Simplify the right side.

Simplify $\frac{\sqrt{2 (- 12 + 5 {(- 2)}^{2})}}{2}$ .

Simplify the numerator.

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

$x = \frac{\sqrt{2 (- 12 + 5 \cdot 4)}}{2}$

$y = - 2$

Multiply $5$ by $4$ .

$x = \frac{\sqrt{2 (- 12 + 20)}}{2}$

$y = - 2$

Add $- 12$ and $20$ .

$x = \frac{\sqrt{2 \cdot 8}}{2}$

$y = - 2$

Multiply $2$ by $8$ .

$x = \frac{\sqrt{16}}{2}$

$y = - 2$

Rewrite $16$ as $4^{2}$ .

$x = \frac{\sqrt{4^{2}}}{2}$

$y = - 2$

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

$x = \frac{4}{2}$

$y = - 2$

$x = \frac{4}{2}$

$y = - 2$

Divide $4$ by $2$ .

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

$x = 2$

$y = - 2$

Step 3

Solve the system $x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}, 5 x^{2} + 2 y^{2} = 28$ .

Replace all occurrences of $x$ with $- \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ in each equation.

Replace all occurrences of $x$ in $5 x^{2} + 2 y^{2} = 28$ with $- \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ .

$5 {(- \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2})}^{2} + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the left side.

Simplify $5 {(- \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2})}^{2} + 2 y^{2}$ .

Simplify each term.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ .

$5 ({(- 1)}^{2} {(\frac{\sqrt{2 (- 12 + 5 y^{2})}}{2})}^{2}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Apply the product rule to $\frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ .

$5 ({(- 1)}^{2} (\frac{{\sqrt{2 (- 12 + 5 y^{2})}}^{2}}{2^{2}})) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 ({(- 1)}^{2} (\frac{{\sqrt{2 (- 12 + 5 y^{2})}}^{2}}{2^{2}})) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$5 (1 (\frac{{\sqrt{2 (- 12 + 5 y^{2})}}^{2}}{2^{2}})) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $\frac{{\sqrt{2 (- 12 + 5 y^{2})}}^{2}}{2^{2}}$ by $1$ .

$5 (\frac{{\sqrt{2 (- 12 + 5 y^{2})}}^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the numerator.

Rewrite ${\sqrt{2 (- 12 + 5 y^{2})}}^{2}$ as $2 (- 12 + 5 y^{2})$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 (- 12 + 5 y^{2})}$ as ${(2 (- 12 + 5 y^{2}))}^{\frac{1}{2}}$ .

$5 (\frac{{({(2 (- 12 + 5 y^{2}))}^{\frac{1}{2}})}^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$5 (\frac{{(2 (- 12 + 5 y^{2}))}^{\frac{1}{2} \cdot 2}}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$5 (\frac{{(2 (- 12 + 5 y^{2}))}^{\frac{2}{2}}}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$5 (\frac{{(2 (- 12 + 5 y^{2}))}^{\frac{2}{2}}}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Rewrite the expression.

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify.

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Apply the distributive property.

$5 (\frac{2 \cdot - 12 + 2 (5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $2$ by $- 12$ .

$5 (\frac{- 24 + 2 (5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $5$ by $2$ .

$5 (\frac{- 24 + 10 y^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $- 24 + 10 y^{2}$ .

Factor $2$ out of $- 24$ .

$5 (\frac{2 (- 12) + 10 y^{2}}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $10 y^{2}$ .

$5 (\frac{2 (- 12) + 2 (5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $2 (- 12) + 2 (5 y^{2})$ .

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{2 (- 12 + 5 y^{2})}{2^{2}}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$5 (\frac{2 (- 12 + 5 y^{2})}{4}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factors.

Factor $2$ out of $4$ .

$5 (\frac{2 (- 12 + 5 y^{2})}{2 \cdot 2}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factor.

$5 (\frac{2 (- 12 + 5 y^{2})}{2 \cdot 2}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Rewrite the expression.

$5 (\frac{- 12 + 5 y^{2}}{2}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$5 (\frac{- 12 + 5 y^{2}}{2}) + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Combine $5$ and $\frac{- 12 + 5 y^{2}}{2}$ .

$\frac{5 (- 12 + 5 y^{2})}{2} + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$\frac{5 (- 12 + 5 y^{2})}{2} + 2 y^{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

To write $2 y^{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 (- 12 + 5 y^{2})}{2} + 2 y^{2} \cdot \frac{2}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify terms.

Combine $2 y^{2}$ and $\frac{2}{2}$ .

$\frac{5 (- 12 + 5 y^{2})}{2} + \frac{2 y^{2} \cdot 2}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Combine the numerators over the common denominator.

$\frac{5 (- 12 + 5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$\frac{5 (- 12 + 5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 \cdot - 12 + 5 (5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $5$ by $- 12$ .

$\frac{- 60 + 5 (5 y^{2}) + 2 y^{2} \cdot 2}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $5$ by $5$ .

$\frac{- 60 + 25 y^{2} + 2 y^{2} \cdot 2}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $2$ by $2$ .

$\frac{- 60 + 25 y^{2} + 4 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Add $25 y^{2}$ and $4 y^{2}$ .

$\frac{- 60 + 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$\frac{- 60 + 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify with factoring out.

Rewrite $- 60$ as $- 1 (60)$ .

$\frac{- 1 \cdot 60 + 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $- 1$ out of $29 y^{2}$ .

$\frac{- 1 \cdot 60 - (- 29 y^{2})}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $- 1$ out of $- 1 (60) - (- 29 y^{2})$ .

$\frac{- 1 (60 - 29 y^{2})}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Move the negative in front of the fraction.

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- \frac{60 - 29 y^{2}}{2} = 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Solve for $y$ in $- \frac{60 - 29 y^{2}}{2} = 28$ .

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{60 - 29 y^{2}}{2}) = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{60 - 29 y^{2}}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{60 - 29 y^{2}}{2}$ into the numerator.

$- 2 \frac{- (60 - 29 y^{2})}{2} = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- (60 - 29 y^{2})}{2}) = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Cancel the common factor.

$2 \cdot (- 1 \frac{- (60 - 29 y^{2})}{2}) = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Rewrite the expression.

$60 - 29 y^{2} = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (60 - 29 y^{2}) = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Multiply $60 - 29 y^{2}$ by $1$ .

$60 - 29 y^{2} = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 2 \cdot 28$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the right side.

Multiply $- 2$ by $28$ .

$60 - 29 y^{2} = - 56$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 56$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$60 - 29 y^{2} = - 56$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

Subtract $60$ from both sides of the equation.

$- 29 y^{2} = - 56 - 60$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Subtract $60$ from $- 56$ .

$- 29 y^{2} = - 116$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$- 29 y^{2} = - 116$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Divide each term in $- 29 y^{2} = - 116$ by $- 29$ and simplify.

Divide each term in $- 29 y^{2} = - 116$ by $- 29$ .

$\frac{- 29 y^{2}}{- 29} = \frac{- 116}{- 29}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the left side.

Cancel the common factor of $- 29$ .

Cancel the common factor.

$\frac{- 29 y^{2}}{- 29} = \frac{- 116}{- 29}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y^{2} = \frac{- 116}{- 29}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = \frac{- 116}{- 29}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = \frac{- 116}{- 29}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify the right side.

Divide $- 116$ by $- 29$ .

$y^{2} = 4$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = 4$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y^{2} = 4$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = \pm \sqrt{4}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$y = \pm \sqrt{2^{2}}$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = \pm 2$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y = \pm 2$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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.

$y = 2$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = - 2$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

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

$y = 2, - 2$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y = 2, - 2$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

$y = 2, - 2$

$x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ with $2$ .

$x = - \frac{\sqrt{2 (- 12 + 5 {(2)}^{2})}}{2}$

$y = 2$

Simplify the right side.

Simplify $- \frac{\sqrt{2 (- 12 + 5 {(2)}^{2})}}{2}$ .

Simplify the numerator.

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

$x = - \frac{\sqrt{2 (- 12 + 5 \cdot 4)}}{2}$

$y = 2$

Multiply $5$ by $4$ .

$x = - \frac{\sqrt{2 (- 12 + 20)}}{2}$

$y = 2$

Add $- 12$ and $20$ .

$x = - \frac{\sqrt{2 \cdot 8}}{2}$

$y = 2$

Multiply $2$ by $8$ .

$x = - \frac{\sqrt{16}}{2}$

$y = 2$

Rewrite $16$ as $4^{2}$ .

$x = - \frac{\sqrt{4^{2}}}{2}$

$y = 2$

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

$x = - \frac{4}{2}$

$y = 2$

$x = - \frac{4}{2}$

$y = 2$

Simplify the expression.

Divide $4$ by $2$ .

$x = - 1 \cdot 2$

$y = 2$

Multiply $- 1$ by $2$ .

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

Replace all occurrences of $y$ with $- 2$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{\sqrt{2 (- 12 + 5 y^{2})}}{2}$ with $- 2$ .

$x = - \frac{\sqrt{2 (- 12 + 5 {(- 2)}^{2})}}{2}$

$y = - 2$

Simplify the right side.

Simplify $- \frac{\sqrt{2 (- 12 + 5 {(- 2)}^{2})}}{2}$ .

Simplify the numerator.

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

$x = - \frac{\sqrt{2 (- 12 + 5 \cdot 4)}}{2}$

$y = - 2$

Multiply $5$ by $4$ .

$x = - \frac{\sqrt{2 (- 12 + 20)}}{2}$

$y = - 2$

Add $- 12$ and $20$ .

$x = - \frac{\sqrt{2 \cdot 8}}{2}$

$y = - 2$

Multiply $2$ by $8$ .

$x = - \frac{\sqrt{16}}{2}$

$y = - 2$

Rewrite $16$ as $4^{2}$ .

$x = - \frac{\sqrt{4^{2}}}{2}$

$y = - 2$

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

$x = - \frac{4}{2}$

$y = - 2$

$x = - \frac{4}{2}$

$y = - 2$

Simplify the expression.

Divide $4$ by $2$ .

$x = - 1 \cdot 2$

$y = - 2$

Multiply $- 1$ by $2$ .

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

Step 4

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

$(2, 2)$

$(2, - 2)$

$(- 2, 2)$

$(- 2, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 2), (2, - 2), (- 2, 2), (- 2, - 2)$

Equation Form:

$x = 2, y = 2$

$x = 2, y = - 2$

$x = - 2, y = 2$

$x = - 2, y = - 2$

Step 6

Solve by Substitution 2x^2-5y^2=-12 , 5x^2+2y^2=28

Related Questions

Support LCMGCF.com by disabling your adblocker.