Precalculus Examples

$7 x^{2} + 3 y^{2} = 187$ , $3 y^{2} - 7 x = 47$

Step 1

Solve for $x$ in $3 y^{2} - 7 x = 47$ .

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Step 1.1

Subtract $3 y^{2}$ from both sides of the equation.

$- 7 x = 47 - 3 y^{2}$

$7 x^{2} + 3 y^{2} = 187$

Step 1.2

Divide each term in $- 7 x = 47 - 3 y^{2}$ by $- 7$ and simplify.

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Step 1.2.1

Divide each term in $- 7 x = 47 - 3 y^{2}$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{47}{- 7} + \frac{- 3 y^{2}}{- 7}$

$7 x^{2} + 3 y^{2} = 187$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 7$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{47}{- 7} + \frac{- 3 y^{2}}{- 7}$

$7 x^{2} + 3 y^{2} = 187$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{47}{- 7} + \frac{- 3 y^{2}}{- 7}$

$7 x^{2} + 3 y^{2} = 187$

$x = \frac{47}{- 7} + \frac{- 3 y^{2}}{- 7}$

$7 x^{2} + 3 y^{2} = 187$

$x = \frac{47}{- 7} + \frac{- 3 y^{2}}{- 7}$

$7 x^{2} + 3 y^{2} = 187$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$x = - \frac{47}{7} + \frac{- 3 y^{2}}{- 7}$

$7 x^{2} + 3 y^{2} = 187$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 x^{2} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 x^{2} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 x^{2} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 x^{2} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 x^{2} + 3 y^{2} = 187$

Step 2

Replace all occurrences of $x$ with $- \frac{47}{7} + \frac{3 y^{2}}{7}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $7 x^{2} + 3 y^{2} = 187$ with $- \frac{47}{7} + \frac{3 y^{2}}{7}$ .

$7 {(- \frac{47}{7} + \frac{3 y^{2}}{7})}^{2} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $7 {(- \frac{47}{7} + \frac{3 y^{2}}{7})}^{2} + 3 y^{2}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Rewrite ${(- \frac{47}{7} + \frac{3 y^{2}}{7})}^{2}$ as $(- \frac{47}{7} + \frac{3 y^{2}}{7}) (- \frac{47}{7} + \frac{3 y^{2}}{7})$ .

$7 ((- \frac{47}{7} + \frac{3 y^{2}}{7}) (- \frac{47}{7} + \frac{3 y^{2}}{7})) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.2

Expand $(- \frac{47}{7} + \frac{3 y^{2}}{7}) (- \frac{47}{7} + \frac{3 y^{2}}{7})$ using the FOIL Method.

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Step 2.2.1.1.2.1

Apply the distributive property.

$7 (- \frac{47}{7} \cdot (- \frac{47}{7} + \frac{3 y^{2}}{7}) + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7} + \frac{3 y^{2}}{7})) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.2.2

Apply the distributive property.

$7 (- \frac{47}{7} \cdot (- \frac{47}{7}) - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7} + \frac{3 y^{2}}{7})) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.2.3

Apply the distributive property.

$7 (- \frac{47}{7} \cdot (- \frac{47}{7}) - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (- \frac{47}{7} \cdot (- \frac{47}{7}) - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3

Simplify and combine like terms.

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Step 2.2.1.1.3.1

Simplify each term.

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Step 2.2.1.1.3.1.1

Multiply $- \frac{47}{7} (- \frac{47}{7})$ .

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Step 2.2.1.1.3.1.1.1

Multiply $- 1$ by $- 1$ .

$7 (1 (\frac{47}{7}) \cdot \frac{47}{7} - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.1.2

Multiply $\frac{47}{7}$ by $1$ .

$7 (\frac{47}{7} \cdot \frac{47}{7} - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.1.3

Multiply $\frac{47}{7}$ by $\frac{47}{7}$ .

$7 (\frac{47 \cdot 47}{7 \cdot 7} - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.1.4

Multiply $47$ by $47$ .

$7 (\frac{2209}{7 \cdot 7} - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.1.5

Multiply $7$ by $7$ .

$7 (\frac{2209}{49} - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} - \frac{47}{7} \cdot \frac{3 y^{2}}{7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.2

Multiply $- \frac{47}{7} \cdot \frac{3 y^{2}}{7}$ .

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Step 2.2.1.1.3.1.2.1

Multiply $\frac{3 y^{2}}{7}$ by $\frac{47}{7}$ .

$7 (\frac{2209}{49} - \frac{3 y^{2} \cdot 47}{7 \cdot 7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.2.2

Multiply $47$ by $3$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{7 \cdot 7} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.2.3

Multiply $7$ by $7$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{2}}{7} \cdot (- \frac{47}{7}) + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.3

Multiply $\frac{3 y^{2}}{7} (- \frac{47}{7})$ .

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Step 2.2.1.1.3.1.3.1

Multiply $\frac{3 y^{2}}{7}$ by $\frac{47}{7}$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{3 y^{2} \cdot 47}{7 \cdot 7} + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.3.2

Multiply $47$ by $3$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{7 \cdot 7} + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.3.3

Multiply $7$ by $7$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{2}}{7} \cdot \frac{3 y^{2}}{7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.4

Combine.

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{2} (3 y^{2})}{7 \cdot 7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.5

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

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Step 2.2.1.1.3.1.5.1

Move $y^{2}$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{3 (y^{2} y^{2}) \cdot 3}{7 \cdot 7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.5.2

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

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{2 + 2} \cdot 3}{7 \cdot 7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.5.3

Add $2$ and $2$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{4} \cdot 3}{7 \cdot 7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{3 y^{4} \cdot 3}{7 \cdot 7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.6

Multiply $3$ by $3$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{9 y^{4}}{7 \cdot 7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.1.7

Multiply $7$ by $7$ .

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} - \frac{141 y^{2}}{49} - \frac{141 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.3.2

Subtract $\frac{141 y^{2}}{49}$ from $- \frac{141 y^{2}}{49}$ .

$7 (\frac{2209}{49} - 2 \frac{141 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} - 2 \frac{141 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.4

Simplify each term.

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Step 2.2.1.1.4.1

Multiply $- 2 \frac{141 y^{2}}{49}$ .

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Step 2.2.1.1.4.1.1

Combine $- 2$ and $\frac{141 y^{2}}{49}$ .

$7 (\frac{2209}{49} + \frac{- 2 (141 y^{2})}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.4.1.2

Multiply $141$ by $- 2$ .

$7 (\frac{2209}{49} + \frac{- 282 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} + \frac{- 282 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.4.2

Move the negative in front of the fraction.

$7 (\frac{2209}{49} - \frac{282 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$7 (\frac{2209}{49} - \frac{282 y^{2}}{49} + \frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.5

Apply the distributive property.

$7 (\frac{2209}{49}) + 7 (- \frac{282 y^{2}}{49}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6

Simplify.

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Step 2.2.1.1.6.1

Cancel the common factor of $7$ .

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Step 2.2.1.1.6.1.1

Factor $7$ out of $49$ .

$7 (\frac{2209}{7 (7)}) + 7 (- \frac{282 y^{2}}{49}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.1.2

Cancel the common factor.

$7 (\frac{2209}{7 \cdot 7}) + 7 (- \frac{282 y^{2}}{49}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.1.3

Rewrite the expression.

$\frac{2209}{7} + 7 (- \frac{282 y^{2}}{49}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{2209}{7} + 7 (- \frac{282 y^{2}}{49}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.2

Cancel the common factor of $7$ .

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Step 2.2.1.1.6.2.1

Move the leading negative in $- \frac{282 y^{2}}{49}$ into the numerator.

$\frac{2209}{7} + 7 (\frac{- 282 y^{2}}{49}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.2.2

Factor $7$ out of $49$ .

$\frac{2209}{7} + 7 (\frac{- 282 y^{2}}{7 (7)}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.2.3

Cancel the common factor.

$\frac{2209}{7} + 7 (\frac{- 282 y^{2}}{7 \cdot 7}) + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.2.4

Rewrite the expression.

$\frac{2209}{7} + \frac{- 282 y^{2}}{7} + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{2209}{7} + \frac{- 282 y^{2}}{7} + 7 (\frac{9 y^{4}}{49}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.3

Cancel the common factor of $7$ .

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Step 2.2.1.1.6.3.1

Factor $7$ out of $49$ .

$\frac{2209}{7} + \frac{- 282 y^{2}}{7} + 7 (\frac{9 y^{4}}{7 (7)}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.3.2

Cancel the common factor.

$\frac{2209}{7} + \frac{- 282 y^{2}}{7} + 7 (\frac{9 y^{4}}{7 \cdot 7}) + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.6.3.3

Rewrite the expression.

$\frac{2209}{7} + \frac{- 282 y^{2}}{7} + \frac{9 y^{4}}{7} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{2209}{7} + \frac{- 282 y^{2}}{7} + \frac{9 y^{4}}{7} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{2209}{7} + \frac{- 282 y^{2}}{7} + \frac{9 y^{4}}{7} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.1.7

Move the negative in front of the fraction.

$\frac{2209}{7} - \frac{282 y^{2}}{7} + \frac{9 y^{4}}{7} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{2209}{7} - \frac{282 y^{2}}{7} + \frac{9 y^{4}}{7} + 3 y^{2} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.2

To write $3 y^{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2209}{7} + \frac{9 y^{4}}{7} - \frac{282 y^{2}}{7} + 3 y^{2} \cdot \frac{7}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.3

Combine $3 y^{2}$ and $\frac{7}{7}$ .

$\frac{2209}{7} + \frac{9 y^{4}}{7} - \frac{282 y^{2}}{7} + \frac{3 y^{2} \cdot 7}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{2209}{7} + \frac{9 y^{4}}{7} + \frac{- 282 y^{2} + 3 y^{2} \cdot 7}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.5

Combine the numerators over the common denominator.

$\frac{2209 + 9 y^{4} - 282 y^{2} + 3 y^{2} \cdot 7}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.6

Multiply $7$ by $3$ .

$\frac{2209 + 9 y^{4} - 282 y^{2} + 21 y^{2}}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.7

Add $- 282 y^{2}$ and $21 y^{2}$ .

$\frac{2209 + 9 y^{4} - 261 y^{2}}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 2.2.1.8

Reorder terms.

$\frac{9 y^{4} - 261 y^{2} + 2209}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{9 y^{4} - 261 y^{2} + 2209}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{9 y^{4} - 261 y^{2} + 2209}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$\frac{9 y^{4} - 261 y^{2} + 2209}{7} = 187$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3

Solve for $y$ in $\frac{9 y^{4} - 261 y^{2} + 2209}{7} = 187$ .

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Step 3.1

Multiply both sides by $7$ .

$\frac{9 y^{4} - 261 y^{2} + 2209}{7} \cdot 7 = 187 \cdot 7$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $7$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{9 y^{4} - 261 y^{2} + 2209}{7} \cdot 7 = 187 \cdot 7$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.2.1.1.2

Rewrite the expression.

$9 y^{4} - 261 y^{2} + 2209 = 187 \cdot 7$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 y^{4} - 261 y^{2} + 2209 = 187 \cdot 7$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 y^{4} - 261 y^{2} + 2209 = 187 \cdot 7$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $187$ by $7$ .

$9 y^{4} - 261 y^{2} + 2209 = 1309$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 y^{4} - 261 y^{2} + 2209 = 1309$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 y^{4} - 261 y^{2} + 2209 = 1309$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3

Solve for $y$ .

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Step 3.3.1

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

$9 u^{2} - 261 u + 2209 = 1309$

$u = y^{2}$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.2

Subtract $1309$ from both sides of the equation.

$9 u^{2} - 261 u + 2209 - 1309 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.3

Subtract $1309$ from $2209$ .

$9 u^{2} - 261 u + 900 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4

Factor the left side of the equation.

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Step 3.3.4.1

Factor $9$ out of $9 u^{2} - 261 u + 900$ .

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Step 3.3.4.1.1

Factor $9$ out of $9 u^{2}$ .

$9 (u^{2}) - 261 u + 900 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4.1.2

Factor $9$ out of $- 261 u$ .

$9 (u^{2}) + 9 (- 29 u) + 900 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4.1.3

Factor $9$ out of $900$ .

$9 u^{2} + 9 (- 29 u) + 9 \cdot 100 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4.1.4

Factor $9$ out of $9 u^{2} + 9 (- 29 u)$ .

$9 (u^{2} - 29 u) + 9 \cdot 100 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4.1.5

Factor $9$ out of $9 (u^{2} - 29 u) + 9 \cdot 100$ .

$9 (u^{2} - 29 u + 100) = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 (u^{2} - 29 u + 100) = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4.2

Factor.

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Step 3.3.4.2.1

Factor $u^{2} - 29 u + 100$ using the AC method.

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Step 3.3.4.2.1.1

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 $100$ and whose sum is $- 29$ .

$- 25, - 4$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4.2.1.2

Write the factored form using these integers.

$9 ((u - 25) (u - 4)) = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 ((u - 25) (u - 4)) = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.4.2.2

Remove unnecessary parentheses.

$9 (u - 25) (u - 4) = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 (u - 25) (u - 4) = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$9 (u - 25) (u - 4) = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.5

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

$u - 25 = 0$

$u - 4 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.6

Set $u - 25$ equal to $0$ and solve for $u$ .

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Step 3.3.6.1

Set $u - 25$ equal to $0$ .

$u - 25 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.6.2

Add $25$ to both sides of the equation.

$u = 25$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$u = 25$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.7

Set $u - 4$ equal to $0$ and solve for $u$ .

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Step 3.3.7.1

Set $u - 4$ equal to $0$ .

$u - 4 = 0$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.7.2

Add $4$ to both sides of the equation.

$u = 4$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$u = 4$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.8

The final solution is all the values that make $9 (u - 25) (u - 4) = 0$ true.

$u = 25, 4$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.9

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

$y^{2} = 25$

$y^{2} = 4$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.10

Solve the first equation for $y$ .

$y^{2} = 25$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.11

Solve the equation for $y$ .

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Step 3.3.11.1

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

$y = \pm \sqrt{25}$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.11.2

Simplify $\pm \sqrt{25}$ .

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Step 3.3.11.2.1

Rewrite $25$ as $5^{2}$ .

$y = \pm \sqrt{5^{2}}$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.11.2.2

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

$y = \pm 5$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = \pm 5$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.11.3

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

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Step 3.3.11.3.1

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

$y = 5$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.11.3.2

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

$y = - 5$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.11.3.3

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

$y = 5, - 5$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = 5, - 5$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = 5, - 5$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.12

Solve the second equation for $y$ .

$y^{2} = 4$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.13

Solve the equation for $y$ .

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Step 3.3.13.1

Remove parentheses.

$y^{2} = 4$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.13.2

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

$y = \pm \sqrt{4}$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.13.3

Simplify $\pm \sqrt{4}$ .

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Step 3.3.13.3.1

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

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

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.13.3.2

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

$y = \pm 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = \pm 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.13.4

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

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Step 3.3.13.4.1

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

$y = 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.13.4.2

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

$y = - 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.13.4.3

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

$y = 2, - 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = 2, - 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = 2, - 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 3.3.14

The solution to $9 y^{4} - 261 y^{2} + 2209 = 1309$ is $y = 5, - 5, 2, - 2$ .

$y = 5, - 5, 2, - 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = 5, - 5, 2, - 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

$y = 5, - 5, 2, - 2$

$x = - \frac{47}{7} + \frac{3 y^{2}}{7}$

Step 4

Replace all occurrences of $y$ with $5$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $5$ .

$x = - \frac{47}{7} + \frac{3 {(5)}^{2}}{7}$

$y = 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{47}{7} + \frac{3 {(5)}^{2}}{7}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(5)}^{2}}{7}$

$y = 5$

Step 4.2.1.2

Simplify each term.

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Step 4.2.1.2.1

Raise $5$ to the power of $2$ .

$x = \frac{- 47 + 3 \cdot 25}{7}$

$y = 5$

Step 4.2.1.2.2

Multiply $3$ by $25$ .

$x = \frac{- 47 + 75}{7}$

$y = 5$

$x = \frac{- 47 + 75}{7}$

$y = 5$

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Add $- 47$ and $75$ .

$x = \frac{28}{7}$

$y = 5$

Step 4.2.1.3.2

Divide $28$ by $7$ .

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

Step 5

Replace all occurrences of $y$ with $- 5$ in each equation.

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Step 5.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $- 5$ .

$x = - \frac{47}{7} + \frac{3 {(- 5)}^{2}}{7}$

$y = - 5$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{47}{7} + \frac{3 {(- 5)}^{2}}{7}$ .

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Step 5.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(- 5)}^{2}}{7}$

$y = - 5$

Step 5.2.1.2

Simplify each term.

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Step 5.2.1.2.1

Raise $- 5$ to the power of $2$ .

$x = \frac{- 47 + 3 \cdot 25}{7}$

$y = - 5$

Step 5.2.1.2.2

Multiply $3$ by $25$ .

$x = \frac{- 47 + 75}{7}$

$y = - 5$

$x = \frac{- 47 + 75}{7}$

$y = - 5$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Add $- 47$ and $75$ .

$x = \frac{28}{7}$

$y = - 5$

Step 5.2.1.3.2

Divide $28$ by $7$ .

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

Step 6

Replace all occurrences of $y$ with $5$ in each equation.

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Step 6.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $5$ .

$x = - \frac{47}{7} + \frac{3 {(5)}^{2}}{7}$

$y = 5$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{47}{7} + \frac{3 {(5)}^{2}}{7}$ .

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Step 6.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(5)}^{2}}{7}$

$y = 5$

Step 6.2.1.2

Simplify each term.

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Step 6.2.1.2.1

Raise $5$ to the power of $2$ .

$x = \frac{- 47 + 3 \cdot 25}{7}$

$y = 5$

Step 6.2.1.2.2

Multiply $3$ by $25$ .

$x = \frac{- 47 + 75}{7}$

$y = 5$

$x = \frac{- 47 + 75}{7}$

$y = 5$

Step 6.2.1.3

Simplify the expression.

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Step 6.2.1.3.1

Add $- 47$ and $75$ .

$x = \frac{28}{7}$

$y = 5$

Step 6.2.1.3.2

Divide $28$ by $7$ .

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

Step 7

Replace all occurrences of $y$ with $- 5$ in each equation.

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Step 7.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $- 5$ .

$x = - \frac{47}{7} + \frac{3 {(- 5)}^{2}}{7}$

$y = - 5$

Step 7.2

Simplify the right side.

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Step 7.2.1

Simplify $- \frac{47}{7} + \frac{3 {(- 5)}^{2}}{7}$ .

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Step 7.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(- 5)}^{2}}{7}$

$y = - 5$

Step 7.2.1.2

Simplify each term.

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Step 7.2.1.2.1

Raise $- 5$ to the power of $2$ .

$x = \frac{- 47 + 3 \cdot 25}{7}$

$y = - 5$

Step 7.2.1.2.2

Multiply $3$ by $25$ .

$x = \frac{- 47 + 75}{7}$

$y = - 5$

$x = \frac{- 47 + 75}{7}$

$y = - 5$

Step 7.2.1.3

Simplify the expression.

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Step 7.2.1.3.1

Add $- 47$ and $75$ .

$x = \frac{28}{7}$

$y = - 5$

Step 7.2.1.3.2

Divide $28$ by $7$ .

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

Step 8

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

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Step 8.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $2$ .

$x = - \frac{47}{7} + \frac{3 {(2)}^{2}}{7}$

$y = 2$

Step 8.2

Simplify the right side.

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Step 8.2.1

Simplify $- \frac{47}{7} + \frac{3 {(2)}^{2}}{7}$ .

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Step 8.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(2)}^{2}}{7}$

$y = 2$

Step 8.2.1.2

Simplify each term.

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Step 8.2.1.2.1

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

$x = \frac{- 47 + 3 \cdot 4}{7}$

$y = 2$

Step 8.2.1.2.2

Multiply $3$ by $4$ .

$x = \frac{- 47 + 12}{7}$

$y = 2$

$x = \frac{- 47 + 12}{7}$

$y = 2$

Step 8.2.1.3

Simplify the expression.

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Step 8.2.1.3.1

Add $- 47$ and $12$ .

$x = \frac{- 35}{7}$

$y = 2$

Step 8.2.1.3.2

Divide $- 35$ by $7$ .

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

Step 9

Replace all occurrences of $y$ with $5$ in each equation.

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Step 9.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $5$ .

$x = - \frac{47}{7} + \frac{3 {(5)}^{2}}{7}$

$y = 5$

Step 9.2

Simplify the right side.

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Step 9.2.1

Simplify $- \frac{47}{7} + \frac{3 {(5)}^{2}}{7}$ .

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Step 9.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(5)}^{2}}{7}$

$y = 5$

Step 9.2.1.2

Simplify each term.

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Step 9.2.1.2.1

Raise $5$ to the power of $2$ .

$x = \frac{- 47 + 3 \cdot 25}{7}$

$y = 5$

Step 9.2.1.2.2

Multiply $3$ by $25$ .

$x = \frac{- 47 + 75}{7}$

$y = 5$

$x = \frac{- 47 + 75}{7}$

$y = 5$

Step 9.2.1.3

Simplify the expression.

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Step 9.2.1.3.1

Add $- 47$ and $75$ .

$x = \frac{28}{7}$

$y = 5$

Step 9.2.1.3.2

Divide $28$ by $7$ .

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

$x = 4$

$y = 5$

Step 10

Replace all occurrences of $y$ with $- 5$ in each equation.

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Step 10.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $- 5$ .

$x = - \frac{47}{7} + \frac{3 {(- 5)}^{2}}{7}$

$y = - 5$

Step 10.2

Simplify the right side.

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Step 10.2.1

Simplify $- \frac{47}{7} + \frac{3 {(- 5)}^{2}}{7}$ .

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Step 10.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(- 5)}^{2}}{7}$

$y = - 5$

Step 10.2.1.2

Simplify each term.

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Step 10.2.1.2.1

Raise $- 5$ to the power of $2$ .

$x = \frac{- 47 + 3 \cdot 25}{7}$

$y = - 5$

Step 10.2.1.2.2

Multiply $3$ by $25$ .

$x = \frac{- 47 + 75}{7}$

$y = - 5$

$x = \frac{- 47 + 75}{7}$

$y = - 5$

Step 10.2.1.3

Simplify the expression.

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Step 10.2.1.3.1

Add $- 47$ and $75$ .

$x = \frac{28}{7}$

$y = - 5$

Step 10.2.1.3.2

Divide $28$ by $7$ .

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

$x = 4$

$y = - 5$

Step 11

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

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Step 11.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $2$ .

$x = - \frac{47}{7} + \frac{3 {(2)}^{2}}{7}$

$y = 2$

Step 11.2

Simplify the right side.

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Step 11.2.1

Simplify $- \frac{47}{7} + \frac{3 {(2)}^{2}}{7}$ .

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Step 11.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(2)}^{2}}{7}$

$y = 2$

Step 11.2.1.2

Simplify each term.

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Step 11.2.1.2.1

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

$x = \frac{- 47 + 3 \cdot 4}{7}$

$y = 2$

Step 11.2.1.2.2

Multiply $3$ by $4$ .

$x = \frac{- 47 + 12}{7}$

$y = 2$

$x = \frac{- 47 + 12}{7}$

$y = 2$

Step 11.2.1.3

Simplify the expression.

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Step 11.2.1.3.1

Add $- 47$ and $12$ .

$x = \frac{- 35}{7}$

$y = 2$

Step 11.2.1.3.2

Divide $- 35$ by $7$ .

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

$x = - 5$

$y = 2$

Step 12

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

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Step 12.1

Replace all occurrences of $y$ in $x = - \frac{47}{7} + \frac{3 y^{2}}{7}$ with $- 2$ .

$x = - \frac{47}{7} + \frac{3 {(- 2)}^{2}}{7}$

$y = - 2$

Step 12.2

Simplify the right side.

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Step 12.2.1

Simplify $- \frac{47}{7} + \frac{3 {(- 2)}^{2}}{7}$ .

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Step 12.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 47 + 3 {(- 2)}^{2}}{7}$

$y = - 2$

Step 12.2.1.2

Simplify each term.

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Step 12.2.1.2.1

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

$x = \frac{- 47 + 3 \cdot 4}{7}$

$y = - 2$

Step 12.2.1.2.2

Multiply $3$ by $4$ .

$x = \frac{- 47 + 12}{7}$

$y = - 2$

$x = \frac{- 47 + 12}{7}$

$y = - 2$

Step 12.2.1.3

Simplify the expression.

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Step 12.2.1.3.1

Add $- 47$ and $12$ .

$x = \frac{- 35}{7}$

$y = - 2$

Step 12.2.1.3.2

Divide $- 35$ by $7$ .

$x = - 5$

$y = - 2$

$x = - 5$

$y = - 2$

$x = - 5$

$y = - 2$

$x = - 5$

$y = - 2$

$x = - 5$

$y = - 2$

Step 13

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

$(4, 5)$

$(4, - 5)$

$(- 5, 2)$

$(- 5, - 2)$

Step 14

The result can be shown in multiple forms.

Point Form:

$(4, 5), (4, - 5), (- 5, 2), (- 5, - 2)$

Equation Form:

$x = 4, y = 5$

$x = 4, y = - 5$

$x = - 5, y = 2$

$x = - 5, y = - 2$

Step 15