Precalculus Examples

$x y = 7$ , $7 x^{2} + y^{2} = 56$

Step 1

Divide each term in $x y = 7$ by $y$ and simplify.

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Step 1.1

Divide each term in $x y = 7$ by $y$ .

$\frac{x y}{y} = \frac{7}{y}$

$7 x^{2} + y^{2} = 56$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $y$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{x y}{y} = \frac{7}{y}$

$7 x^{2} + y^{2} = 56$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{y}$

$7 x^{2} + y^{2} = 56$

$x = \frac{7}{y}$

$7 x^{2} + y^{2} = 56$

$x = \frac{7}{y}$

$7 x^{2} + y^{2} = 56$

$x = \frac{7}{y}$

$7 x^{2} + y^{2} = 56$

Step 2

Replace all occurrences of $x$ with $\frac{7}{y}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $7 x^{2} + y^{2} = 56$ with $\frac{7}{y}$ .

$7 {(\frac{7}{y})}^{2} + y^{2} = 56$

$x = \frac{7}{y}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Apply the product rule to $\frac{7}{y}$ .

$7 (\frac{7^{2}}{y^{2}}) + y^{2} = 56$

$x = \frac{7}{y}$

Step 2.2.1.2

Raise $7$ to the power of $2$ .

$7 (\frac{49}{y^{2}}) + y^{2} = 56$

$x = \frac{7}{y}$

Step 2.2.1.3

Multiply $7 \frac{49}{y^{2}}$ .

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Step 2.2.1.3.1

Combine $7$ and $\frac{49}{y^{2}}$ .

$\frac{7 \cdot 49}{y^{2}} + y^{2} = 56$

$x = \frac{7}{y}$

Step 2.2.1.3.2

Multiply $7$ by $49$ .

$\frac{343}{y^{2}} + y^{2} = 56$

$x = \frac{7}{y}$

$\frac{343}{y^{2}} + y^{2} = 56$

$x = \frac{7}{y}$

$\frac{343}{y^{2}} + y^{2} = 56$

$x = \frac{7}{y}$

$\frac{343}{y^{2}} + y^{2} = 56$

$x = \frac{7}{y}$

$\frac{343}{y^{2}} + y^{2} = 56$

$x = \frac{7}{y}$

Step 3

Solve for $y$ in $\frac{343}{y^{2}} + y^{2} = 56$ .

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Step 3.1

Find the LCD of the terms in the equation.

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Step 3.1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y^{2}, 1, 1$

$x = \frac{7}{y}$

Step 3.1.2

The LCM of one and any expression is the expression.

$y^{2}$

$x = \frac{7}{y}$

$y^{2}$

$x = \frac{7}{y}$

Step 3.2

Multiply each term in $\frac{343}{y^{2}} + y^{2} = 56$ by $y^{2}$ to eliminate the fractions.

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Step 3.2.1

Multiply each term in $\frac{343}{y^{2}} + y^{2} = 56$ by $y^{2}$ .

$\frac{343}{y^{2}} \cdot y^{2} + y^{2} y^{2} = 56 y^{2}$

$x = \frac{7}{y}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Simplify each term.

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Step 3.2.2.1.1

Cancel the common factor of $y^{2}$ .

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Step 3.2.2.1.1.1

Cancel the common factor.

$\frac{343}{y^{2}} \cdot y^{2} + y^{2} y^{2} = 56 y^{2}$

$x = \frac{7}{y}$

Step 3.2.2.1.1.2

Rewrite the expression.

$343 + y^{2} y^{2} = 56 y^{2}$

$x = \frac{7}{y}$

$343 + y^{2} y^{2} = 56 y^{2}$

$x = \frac{7}{y}$

Step 3.2.2.1.2

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

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Step 3.2.2.1.2.1

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

$343 + y^{2 + 2} = 56 y^{2}$

$x = \frac{7}{y}$

Step 3.2.2.1.2.2

Add $2$ and $2$ .

$343 + y^{4} = 56 y^{2}$

$x = \frac{7}{y}$

$343 + y^{4} = 56 y^{2}$

$x = \frac{7}{y}$

$343 + y^{4} = 56 y^{2}$

$x = \frac{7}{y}$

$343 + y^{4} = 56 y^{2}$

$x = \frac{7}{y}$

$343 + y^{4} = 56 y^{2}$

$x = \frac{7}{y}$

Step 3.3

Solve the equation.

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Step 3.3.1

Subtract $56 y^{2}$ from both sides of the equation.

$343 + y^{4} - 56 y^{2} = 0$

$x = \frac{7}{y}$

Step 3.3.2

Substitute $u = y^{2}$ into the equation. This will make the quadratic formula easy to use.

$u^{2} - 56 u + 343 = 0$

$u = y^{2}$

$x = \frac{7}{y}$

Step 3.3.3

Factor $u^{2} - 56 u + 343$ using the AC method.

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Step 3.3.3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $343$ and whose sum is $- 56$ .

$- 49, - 7$

$x = \frac{7}{y}$

Step 3.3.3.2

Write the factored form using these integers.

$(u - 49) (u - 7) = 0$

$x = \frac{7}{y}$

$(u - 49) (u - 7) = 0$

$x = \frac{7}{y}$

Step 3.3.4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$u - 49 = 0$

$u - 7 = 0$

$x = \frac{7}{y}$

Step 3.3.5

Set $u - 49$ equal to $0$ and solve for $u$ .

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Step 3.3.5.1

Set $u - 49$ equal to $0$ .

$u - 49 = 0$

$x = \frac{7}{y}$

Step 3.3.5.2

Add $49$ to both sides of the equation.

$u = 49$

$x = \frac{7}{y}$

$u = 49$

$x = \frac{7}{y}$

Step 3.3.6

Set $u - 7$ equal to $0$ and solve for $u$ .

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Step 3.3.6.1

Set $u - 7$ equal to $0$ .

$u - 7 = 0$

$x = \frac{7}{y}$

Step 3.3.6.2

Add $7$ to both sides of the equation.

$u = 7$

$x = \frac{7}{y}$

$u = 7$

$x = \frac{7}{y}$

Step 3.3.7

The final solution is all the values that make $(u - 49) (u - 7) = 0$ true.

$u = 49, 7$

$x = \frac{7}{y}$

Step 3.3.8

Substitute the real value of $u = y^{2}$ back into the solved equation.

$y^{2} = 49$

$y^{2} = 7$

$x = \frac{7}{y}$

Step 3.3.9

Solve the first equation for $y$ .

$y^{2} = 49$

$x = \frac{7}{y}$

Step 3.3.10

Solve the equation for $y$ .

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Step 3.3.10.1

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

$y = \pm \sqrt{49}$

$x = \frac{7}{y}$

Step 3.3.10.2

Simplify $\pm \sqrt{49}$ .

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Step 3.3.10.2.1

Rewrite $49$ as $7^{2}$ .

$y = \pm \sqrt{7^{2}}$

$x = \frac{7}{y}$

Step 3.3.10.2.2

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

$y = \pm 7$

$x = \frac{7}{y}$

$y = \pm 7$

$x = \frac{7}{y}$

Step 3.3.10.3

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

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Step 3.3.10.3.1

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

$y = 7$

$x = \frac{7}{y}$

Step 3.3.10.3.2

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

$y = - 7$

$x = \frac{7}{y}$

Step 3.3.10.3.3

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

$y = 7, - 7$

$x = \frac{7}{y}$

$y = 7, - 7$

$x = \frac{7}{y}$

$y = 7, - 7$

$x = \frac{7}{y}$

Step 3.3.11

Solve the second equation for $y$ .

$y^{2} = 7$

$x = \frac{7}{y}$

Step 3.3.12

Solve the equation for $y$ .

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Step 3.3.12.1

Remove parentheses.

$y^{2} = 7$

$x = \frac{7}{y}$

Step 3.3.12.2

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

$y = \pm \sqrt{7}$

$x = \frac{7}{y}$

Step 3.3.12.3

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

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Step 3.3.12.3.1

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

$y = \sqrt{7}$

$x = \frac{7}{y}$

Step 3.3.12.3.2

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

$y = - \sqrt{7}$

$x = \frac{7}{y}$

Step 3.3.12.3.3

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

$y = \sqrt{7}, - \sqrt{7}$

$x = \frac{7}{y}$

$y = \sqrt{7}, - \sqrt{7}$

$x = \frac{7}{y}$

$y = \sqrt{7}, - \sqrt{7}$

$x = \frac{7}{y}$

Step 3.3.13

The solution to $y^{4} - 56 y^{2} + 343 = 0$ is $y = 7, - 7, \sqrt{7}, - \sqrt{7}$ .

$y = 7, - 7, \sqrt{7}, - \sqrt{7}$

$x = \frac{7}{y}$

$y = 7, - 7, \sqrt{7}, - \sqrt{7}$

$x = \frac{7}{y}$

$y = 7, - 7, \sqrt{7}, - \sqrt{7}$

$x = \frac{7}{y}$

Step 4

Replace all occurrences of $y$ with $7$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $7$ .

$x = \frac{7}{7}$

$y = 7$

Step 4.2

Simplify the right side.

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Step 4.2.1

Divide $7$ by $7$ .

$x = 1$

$y = 7$

$x = 1$

$y = 7$

$x = 1$

$y = 7$

Step 5

Replace all occurrences of $y$ with $- 7$ in each equation.

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Step 5.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $- 7$ .

$x = \frac{7}{- 7}$

$y = - 7$

Step 5.2

Simplify the right side.

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Step 5.2.1

Divide $7$ by $- 7$ .

$x = - 1$

$y = - 7$

$x = - 1$

$y = - 7$

$x = - 1$

$y = - 7$

Step 6

Replace all occurrences of $y$ with $7$ in each equation.

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Step 6.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $7$ .

$x = \frac{7}{7}$

$y = 7$

Step 6.2

Simplify the right side.

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Step 6.2.1

Divide $7$ by $7$ .

$x = 1$

$y = 7$

$x = 1$

$y = 7$

$x = 1$

$y = 7$

Step 7

Replace all occurrences of $y$ with $- 7$ in each equation.

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Step 7.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $- 7$ .

$x = \frac{7}{- 7}$

$y = - 7$

Step 7.2

Simplify the right side.

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Step 7.2.1

Divide $7$ by $- 7$ .

$x = - 1$

$y = - 7$

$x = - 1$

$y = - 7$

$x = - 1$

$y = - 7$

Step 8

Replace all occurrences of $y$ with $\sqrt{7}$ in each equation.

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Step 8.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $\sqrt{7}$ .

$x = \frac{7}{\sqrt{7}}$

$y = \sqrt{7}$

Step 8.2

Simplify the right side.

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Step 8.2.1

Simplify $\frac{7}{\sqrt{7}}$ .

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Step 8.2.1.1

Multiply $\frac{7}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = \frac{7}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

$y = \sqrt{7}$

Step 8.2.1.2

Combine and simplify the denominator.

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Step 8.2.1.2.1

Multiply $\frac{7}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = \sqrt{7}$

Step 8.2.1.2.2

Raise $\sqrt{7}$ to the power of $1$ .

$x = \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = \sqrt{7}$

Step 8.2.1.2.3

Raise $\sqrt{7}$ to the power of $1$ .

$x = \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = \sqrt{7}$

Step 8.2.1.2.4

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

$x = \frac{7 \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

$y = \sqrt{7}$

Step 8.2.1.2.5

Add $1$ and $1$ .

$x = \frac{7 \sqrt{7}}{{\sqrt{7}}^{2}}$

$y = \sqrt{7}$

Step 8.2.1.2.6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 8.2.1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$x = \frac{7 \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

$y = \sqrt{7}$

Step 8.2.1.2.6.2

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

$x = \frac{7 \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

$y = \sqrt{7}$

Step 8.2.1.2.6.3

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

$x = \frac{7 \sqrt{7}}{7^{\frac{2}{2}}}$

$y = \sqrt{7}$

Step 8.2.1.2.6.4

Cancel the common factor of $2$ .

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Step 8.2.1.2.6.4.1

Cancel the common factor.

$x = \frac{7 \sqrt{7}}{7^{\frac{2}{2}}}$

$y = \sqrt{7}$

Step 8.2.1.2.6.4.2

Rewrite the expression.

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

Step 8.2.1.2.6.5

Evaluate the exponent.

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

Step 8.2.1.3

Cancel the common factor of $7$ .

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Step 8.2.1.3.1

Cancel the common factor.

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

Step 8.2.1.3.2

Divide $\sqrt{7}$ by $1$ .

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

Step 9

Replace all occurrences of $y$ with $7$ in each equation.

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Step 9.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $7$ .

$x = \frac{7}{7}$

$y = 7$

Step 9.2

Simplify the right side.

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Step 9.2.1

Divide $7$ by $7$ .

$x = 1$

$y = 7$

$x = 1$

$y = 7$

$x = 1$

$y = 7$

Step 10

Replace all occurrences of $y$ with $- 7$ in each equation.

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Step 10.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $- 7$ .

$x = \frac{7}{- 7}$

$y = - 7$

Step 10.2

Simplify the right side.

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Step 10.2.1

Divide $7$ by $- 7$ .

$x = - 1$

$y = - 7$

$x = - 1$

$y = - 7$

$x = - 1$

$y = - 7$

Step 11

Replace all occurrences of $y$ with $\sqrt{7}$ in each equation.

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Step 11.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $\sqrt{7}$ .

$x = \frac{7}{\sqrt{7}}$

$y = \sqrt{7}$

Step 11.2

Simplify the right side.

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Step 11.2.1

Simplify $\frac{7}{\sqrt{7}}$ .

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Step 11.2.1.1

Multiply $\frac{7}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = \frac{7}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

$y = \sqrt{7}$

Step 11.2.1.2

Combine and simplify the denominator.

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Step 11.2.1.2.1

Multiply $\frac{7}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = \sqrt{7}$

Step 11.2.1.2.2

Raise $\sqrt{7}$ to the power of $1$ .

$x = \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = \sqrt{7}$

Step 11.2.1.2.3

Raise $\sqrt{7}$ to the power of $1$ .

$x = \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = \sqrt{7}$

Step 11.2.1.2.4

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

$x = \frac{7 \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

$y = \sqrt{7}$

Step 11.2.1.2.5

Add $1$ and $1$ .

$x = \frac{7 \sqrt{7}}{{\sqrt{7}}^{2}}$

$y = \sqrt{7}$

Step 11.2.1.2.6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 11.2.1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$x = \frac{7 \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

$y = \sqrt{7}$

Step 11.2.1.2.6.2

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

$x = \frac{7 \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

$y = \sqrt{7}$

Step 11.2.1.2.6.3

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

$x = \frac{7 \sqrt{7}}{7^{\frac{2}{2}}}$

$y = \sqrt{7}$

Step 11.2.1.2.6.4

Cancel the common factor of $2$ .

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Step 11.2.1.2.6.4.1

Cancel the common factor.

$x = \frac{7 \sqrt{7}}{7^{\frac{2}{2}}}$

$y = \sqrt{7}$

Step 11.2.1.2.6.4.2

Rewrite the expression.

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

Step 11.2.1.2.6.5

Evaluate the exponent.

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

Step 11.2.1.3

Cancel the common factor of $7$ .

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Step 11.2.1.3.1

Cancel the common factor.

$x = \frac{7 \sqrt{7}}{7}$

$y = \sqrt{7}$

Step 11.2.1.3.2

Divide $\sqrt{7}$ by $1$ .

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

$x = \sqrt{7}$

$y = \sqrt{7}$

Step 12

Replace all occurrences of $y$ with $- \sqrt{7}$ in each equation.

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Step 12.1

Replace all occurrences of $y$ in $x = \frac{7}{y}$ with $- \sqrt{7}$ .

$x = \frac{7}{- \sqrt{7}}$

$y = - \sqrt{7}$

Step 12.2

Simplify the right side.

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Step 12.2.1

Simplify $\frac{7}{- \sqrt{7}}$ .

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Step 12.2.1.1

Move the negative in front of the fraction.

$x = - \frac{7}{\sqrt{7}}$

$y = - \sqrt{7}$

Step 12.2.1.2

Multiply $\frac{7}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = - (\frac{7}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}})$

$y = - \sqrt{7}$

Step 12.2.1.3

Combine and simplify the denominator.

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Step 12.2.1.3.1

Multiply $\frac{7}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = - \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = - \sqrt{7}$

Step 12.2.1.3.2

Raise $\sqrt{7}$ to the power of $1$ .

$x = - \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = - \sqrt{7}$

Step 12.2.1.3.3

Raise $\sqrt{7}$ to the power of $1$ .

$x = - \frac{7 \sqrt{7}}{\sqrt{7} \sqrt{7}}$

$y = - \sqrt{7}$

Step 12.2.1.3.4

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

$x = - \frac{7 \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

$y = - \sqrt{7}$

Step 12.2.1.3.5

Add $1$ and $1$ .

$x = - \frac{7 \sqrt{7}}{{\sqrt{7}}^{2}}$

$y = - \sqrt{7}$

Step 12.2.1.3.6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 12.2.1.3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$x = - \frac{7 \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

$y = - \sqrt{7}$

Step 12.2.1.3.6.2

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

$x = - \frac{7 \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

$y = - \sqrt{7}$

Step 12.2.1.3.6.3

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

$x = - \frac{7 \sqrt{7}}{7^{\frac{2}{2}}}$

$y = - \sqrt{7}$

Step 12.2.1.3.6.4

Cancel the common factor of $2$ .

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Step 12.2.1.3.6.4.1

Cancel the common factor.

$x = - \frac{7 \sqrt{7}}{7^{\frac{2}{2}}}$

$y = - \sqrt{7}$

Step 12.2.1.3.6.4.2

Rewrite the expression.

$x = - \frac{7 \sqrt{7}}{7}$

$y = - \sqrt{7}$

$x = - \frac{7 \sqrt{7}}{7}$

$y = - \sqrt{7}$

Step 12.2.1.3.6.5

Evaluate the exponent.

$x = - \frac{7 \sqrt{7}}{7}$

$y = - \sqrt{7}$

$x = - \frac{7 \sqrt{7}}{7}$

$y = - \sqrt{7}$

$x = - \frac{7 \sqrt{7}}{7}$

$y = - \sqrt{7}$

Step 12.2.1.4

Cancel the common factor of $7$ .

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Step 12.2.1.4.1

Cancel the common factor.

$x = - \frac{7 \sqrt{7}}{7}$

$y = - \sqrt{7}$

Step 12.2.1.4.2

Divide $\sqrt{7}$ by $1$ .

$x = - \sqrt{7}$

$y = - \sqrt{7}$

$x = - \sqrt{7}$

$y = - \sqrt{7}$

$x = - \sqrt{7}$

$y = - \sqrt{7}$

$x = - \sqrt{7}$

$y = - \sqrt{7}$

$x = - \sqrt{7}$

$y = - \sqrt{7}$

Step 13

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

$(1, 7)$

$(- 1, - 7)$

$(\sqrt{7}, \sqrt{7})$

$(- \sqrt{7}, - \sqrt{7})$

Step 14

The result can be shown in multiple forms.

Point Form:

$(1, 7), (- 1, - 7), (\sqrt{7}, \sqrt{7}), (- \sqrt{7}, - \sqrt{7})$

Equation Form:

$x = 1, y = 7$

$x = - 1, y = - 7$

$x = \sqrt{7}, y = \sqrt{7}$

$x = - \sqrt{7}, y = - \sqrt{7}$

Step 15