Finite Math Examples

$x^{2} + 4 y^{2} = 20$ , $2 x - 3 y - 2 = 0$

Step 1

Solve for $x$ in $2 x - 3 y - 2 = 0$ .

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Step 1.1

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

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Step 1.1.1

Add $3 y$ to both sides of the equation.

$2 x - 2 = 3 y$

$x^{2} + 4 y^{2} = 20$

Step 1.1.2

Add $2$ to both sides of the equation.

$2 x = 3 y + 2$

$x^{2} + 4 y^{2} = 20$

$2 x = 3 y + 2$

$x^{2} + 4 y^{2} = 20$

Step 1.2

Divide each term in $2 x = 3 y + 2$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = 3 y + 2$ by $2$ .

$\frac{2 x}{2} = \frac{3 y}{2} + \frac{2}{2}$

$x^{2} + 4 y^{2} = 20$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3 y}{2} + \frac{2}{2}$

$x^{2} + 4 y^{2} = 20$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3 y}{2} + \frac{2}{2}$

$x^{2} + 4 y^{2} = 20$

$x = \frac{3 y}{2} + \frac{2}{2}$

$x^{2} + 4 y^{2} = 20$

$x = \frac{3 y}{2} + \frac{2}{2}$

$x^{2} + 4 y^{2} = 20$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $2$ by $2$ .

$x = \frac{3 y}{2} + 1$

$x^{2} + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$x^{2} + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$x^{2} + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$x^{2} + 4 y^{2} = 20$

Step 2

Replace all occurrences of $x$ with $\frac{3 y}{2} + 1$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x^{2} + 4 y^{2} = 20$ with $\frac{3 y}{2} + 1$ .

${(\frac{3 y}{2} + 1)}^{2} + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${(\frac{3 y}{2} + 1)}^{2} + 4 y^{2}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Rewrite ${(\frac{3 y}{2} + 1)}^{2}$ as $(\frac{3 y}{2} + 1) (\frac{3 y}{2} + 1)$ .

$(\frac{3 y}{2} + 1) (\frac{3 y}{2} + 1) + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.2

Expand $(\frac{3 y}{2} + 1) (\frac{3 y}{2} + 1)$ using the FOIL Method.

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Step 2.2.1.1.2.1

Apply the distributive property.

$\frac{3 y}{2} \cdot (\frac{3 y}{2} + 1) + 1 (\frac{3 y}{2} + 1) + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.2.2

Apply the distributive property.

$\frac{3 y}{2} \cdot \frac{3 y}{2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2} + 1) + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.2.3

Apply the distributive property.

$\frac{3 y}{2} \cdot \frac{3 y}{2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$\frac{3 y}{2} \cdot \frac{3 y}{2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

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 $\frac{3 y}{2} \cdot \frac{3 y}{2}$ .

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Step 2.2.1.1.3.1.1.1

Multiply $\frac{3 y}{2}$ by $\frac{3 y}{2}$ .

$\frac{3 y (3 y)}{2 \cdot 2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.1.2

Multiply $3$ by $3$ .

$\frac{9 y \cdot y}{2 \cdot 2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.1.3

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

$\frac{9 (y \cdot y)}{2 \cdot 2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.1.4

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

$\frac{9 (y \cdot y)}{2 \cdot 2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.1.5

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

$\frac{9 y^{1 + 1}}{2 \cdot 2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.1.6

Add $1$ and $1$ .

$\frac{9 y^{2}}{2 \cdot 2} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.1.7

Multiply $2$ by $2$ .

$\frac{9 y^{2}}{4} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$\frac{9 y^{2}}{4} + \frac{3 y}{2} \cdot 1 + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.2

Multiply $\frac{3 y}{2}$ by $1$ .

$\frac{9 y^{2}}{4} + \frac{3 y}{2} + 1 (\frac{3 y}{2}) + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.3

Multiply $\frac{3 y}{2}$ by $1$ .

$\frac{9 y^{2}}{4} + \frac{3 y}{2} + \frac{3 y}{2} + 1 \cdot 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.1.4

Multiply $1$ by $1$ .

$\frac{9 y^{2}}{4} + \frac{3 y}{2} + \frac{3 y}{2} + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$\frac{9 y^{2}}{4} + \frac{3 y}{2} + \frac{3 y}{2} + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.3.2

Add $\frac{3 y}{2}$ and $\frac{3 y}{2}$ .

$\frac{9 y^{2}}{4} + 2 (\frac{3 y}{2}) + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$\frac{9 y^{2}}{4} + 2 (\frac{3 y}{2}) + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.4

Cancel the common factor of $2$ .

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Step 2.2.1.1.4.1

Cancel the common factor.

$\frac{9 y^{2}}{4} + 2 (\frac{3 y}{2}) + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.1.4.2

Rewrite the expression.

$\frac{9 y^{2}}{4} + 3 y + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$\frac{9 y^{2}}{4} + 3 y + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

$\frac{9 y^{2}}{4} + 3 y + 1 + 4 y^{2} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.2

To write $4 y^{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$3 y + 1 + \frac{9 y^{2}}{4} + 4 y^{2} \cdot \frac{4}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $4 y^{2}$ and $\frac{4}{4}$ .

$3 y + 1 + \frac{9 y^{2}}{4} + \frac{4 y^{2} \cdot 4}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$3 y + 1 + \frac{9 y^{2} + 4 y^{2} \cdot 4}{4} = 20$

$x = \frac{3 y}{2} + 1$

$3 y + 1 + \frac{9 y^{2} + 4 y^{2} \cdot 4}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.4

Simplify each term.

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Step 2.2.1.4.1

Simplify the numerator.

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Step 2.2.1.4.1.1

Factor $y^{2}$ out of $9 y^{2} + 4 y^{2} \cdot 4$ .

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Step 2.2.1.4.1.1.1

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

$3 y + 1 + \frac{y^{2} \cdot 9 + 4 y^{2} \cdot 4}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.4.1.1.2

Factor $y^{2}$ out of $4 y^{2} \cdot 4$ .

$3 y + 1 + \frac{y^{2} \cdot 9 + y^{2} (4 \cdot 4)}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.4.1.1.3

Factor $y^{2}$ out of $y^{2} \cdot 9 + y^{2} (4 \cdot 4)$ .

$3 y + 1 + \frac{y^{2} (9 + 4 \cdot 4)}{4} = 20$

$x = \frac{3 y}{2} + 1$

$3 y + 1 + \frac{y^{2} (9 + 4 \cdot 4)}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.4.1.2

Multiply $4$ by $4$ .

$3 y + 1 + \frac{y^{2} (9 + 16)}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.4.1.3

Add $9$ and $16$ .

$3 y + 1 + \frac{y^{2} \cdot 25}{4} = 20$

$x = \frac{3 y}{2} + 1$

$3 y + 1 + \frac{y^{2} \cdot 25}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 2.2.1.4.2

Move $25$ to the left of $y^{2}$ .

$3 y + 1 + \frac{25 y^{2}}{4} = 20$

$x = \frac{3 y}{2} + 1$

$3 y + 1 + \frac{25 y^{2}}{4} = 20$

$x = \frac{3 y}{2} + 1$

$3 y + 1 + \frac{25 y^{2}}{4} = 20$

$x = \frac{3 y}{2} + 1$

$3 y + 1 + \frac{25 y^{2}}{4} = 20$

$x = \frac{3 y}{2} + 1$

$3 y + 1 + \frac{25 y^{2}}{4} = 20$

$x = \frac{3 y}{2} + 1$

Step 3

Solve for $y$ in $3 y + 1 + \frac{25 y^{2}}{4} = 20$ .

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Step 3.1

Move all terms to the left side of the equation and simplify.

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Step 3.1.1

Subtract $20$ from both sides of the equation.

$3 y + 1 + \frac{25 y^{2}}{4} - 20 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.1.2

Subtract $20$ from $1$ .

$3 y + \frac{25 y^{2}}{4} - 19 = 0$

$x = \frac{3 y}{2} + 1$

$3 y + \frac{25 y^{2}}{4} - 19 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.2

Multiply through by the least common denominator $4$ , then simplify.

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Step 3.2.1

Apply the distributive property.

$4 (3 y) + 4 (\frac{25 y^{2}}{4}) + 4 \cdot - 19 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.2.2

Simplify.

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Step 3.2.2.1

Multiply $3$ by $4$ .

$12 y + 4 (\frac{25 y^{2}}{4}) + 4 \cdot - 19 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.2.2.2

Cancel the common factor of $4$ .

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Step 3.2.2.2.1

Cancel the common factor.

$12 y + 4 (\frac{25 y^{2}}{4}) + 4 \cdot - 19 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.2.2.2.2

Rewrite the expression.

$12 y + 25 y^{2} + 4 \cdot - 19 = 0$

$x = \frac{3 y}{2} + 1$

$12 y + 25 y^{2} + 4 \cdot - 19 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.2.2.3

Multiply $4$ by $- 19$ .

$12 y + 25 y^{2} - 76 = 0$

$x = \frac{3 y}{2} + 1$

$12 y + 25 y^{2} - 76 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.2.3

Reorder $12 y$ and $25 y^{2}$ .

$25 y^{2} + 12 y - 76 = 0$

$x = \frac{3 y}{2} + 1$

$25 y^{2} + 12 y - 76 = 0$

$x = \frac{3 y}{2} + 1$

Step 3.3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

$x = \frac{3 y}{2} + 1$

Step 3.4

Substitute the values $a = 25$ , $b = 12$ , and $c = - 76$ into the quadratic formula and solve for $y$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (25 \cdot - 76)}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.5

Simplify.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Raise $12$ to the power of $2$ .

$y = \frac{- 12 \pm \sqrt{144 - 4 \cdot 25 \cdot - 76}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.5.1.2

Multiply $- 4 \cdot 25 \cdot - 76$ .

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Step 3.5.1.2.1

Multiply $- 4$ by $25$ .

$y = \frac{- 12 \pm \sqrt{144 - 100 \cdot - 76}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.5.1.2.2

Multiply $- 100$ by $- 76$ .

$y = \frac{- 12 \pm \sqrt{144 + 7600}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{- 12 \pm \sqrt{144 + 7600}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.5.1.3

Add $144$ and $7600$ .

$y = \frac{- 12 \pm \sqrt{7744}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.5.1.4

Rewrite $7744$ as $88^{2}$ .

$y = \frac{- 12 \pm \sqrt{88^{2}}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.5.1.5

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

$y = \frac{- 12 \pm 88}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{- 12 \pm 88}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.5.2

Multiply $2$ by $25$ .

$y = \frac{- 12 \pm 88}{50}$

$x = \frac{3 y}{2} + 1$

Step 3.5.3

Simplify $\frac{- 12 \pm 88}{50}$ .

$y = \frac{- 6 \pm 44}{25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{- 6 \pm 44}{25}$

$x = \frac{3 y}{2} + 1$

Step 3.6

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Raise $12$ to the power of $2$ .

$y = \frac{- 12 \pm \sqrt{144 - 4 \cdot 25 \cdot - 76}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.1.2

Multiply $- 4 \cdot 25 \cdot - 76$ .

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Step 3.6.1.2.1

Multiply $- 4$ by $25$ .

$y = \frac{- 12 \pm \sqrt{144 - 100 \cdot - 76}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.1.2.2

Multiply $- 100$ by $- 76$ .

$y = \frac{- 12 \pm \sqrt{144 + 7600}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{- 12 \pm \sqrt{144 + 7600}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.1.3

Add $144$ and $7600$ .

$y = \frac{- 12 \pm \sqrt{7744}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.1.4

Rewrite $7744$ as $88^{2}$ .

$y = \frac{- 12 \pm \sqrt{88^{2}}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.1.5

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

$y = \frac{- 12 \pm 88}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{- 12 \pm 88}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.2

Multiply $2$ by $25$ .

$y = \frac{- 12 \pm 88}{50}$

$x = \frac{3 y}{2} + 1$

Step 3.6.3

Simplify $\frac{- 12 \pm 88}{50}$ .

$y = \frac{- 6 \pm 44}{25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.4

Change the $\pm$ to $+$ .

$y = \frac{- 6 + 44}{25}$

$x = \frac{3 y}{2} + 1$

Step 3.6.5

Add $- 6$ and $44$ .

$y = \frac{38}{25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{38}{25}$

$x = \frac{3 y}{2} + 1$

Step 3.7

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Step 3.7.1

Simplify the numerator.

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Step 3.7.1.1

Raise $12$ to the power of $2$ .

$y = \frac{- 12 \pm \sqrt{144 - 4 \cdot 25 \cdot - 76}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.1.2

Multiply $- 4 \cdot 25 \cdot - 76$ .

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Step 3.7.1.2.1

Multiply $- 4$ by $25$ .

$y = \frac{- 12 \pm \sqrt{144 - 100 \cdot - 76}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.1.2.2

Multiply $- 100$ by $- 76$ .

$y = \frac{- 12 \pm \sqrt{144 + 7600}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{- 12 \pm \sqrt{144 + 7600}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.1.3

Add $144$ and $7600$ .

$y = \frac{- 12 \pm \sqrt{7744}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.1.4

Rewrite $7744$ as $88^{2}$ .

$y = \frac{- 12 \pm \sqrt{88^{2}}}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.1.5

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

$y = \frac{- 12 \pm 88}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

$y = \frac{- 12 \pm 88}{2 \cdot 25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.2

Multiply $2$ by $25$ .

$y = \frac{- 12 \pm 88}{50}$

$x = \frac{3 y}{2} + 1$

Step 3.7.3

Simplify $\frac{- 12 \pm 88}{50}$ .

$y = \frac{- 6 \pm 44}{25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.4

Change the $\pm$ to $-$ .

$y = \frac{- 6 - 44}{25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.5

Subtract $44$ from $- 6$ .

$y = \frac{- 50}{25}$

$x = \frac{3 y}{2} + 1$

Step 3.7.6

Divide $- 50$ by $25$ .

$y = - 2$

$x = \frac{3 y}{2} + 1$

$y = - 2$

$x = \frac{3 y}{2} + 1$

Step 3.8

The final answer is the combination of both solutions.

$y = \frac{38}{25}, - 2$

$x = \frac{3 y}{2} + 1$

$y = \frac{38}{25}, - 2$

$x = \frac{3 y}{2} + 1$

Step 4

Replace all occurrences of $y$ with $\frac{38}{25}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{3 y}{2} + 1$ with $\frac{38}{25}$ .

$x = \frac{3 (\frac{38}{25})}{2} + 1$

$y = \frac{38}{25}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3 (\frac{38}{25})}{2} + 1$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Combine $3$ and $\frac{38}{25}$ .

$x = \frac{\frac{3 \cdot 38}{25}}{2} + 1$

$y = \frac{38}{25}$

Step 4.2.1.1.2

Multiply $3$ by $38$ .

$x = \frac{\frac{114}{25}}{2} + 1$

$y = \frac{38}{25}$

Step 4.2.1.1.3

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{114}{25} \cdot \frac{1}{2} + 1$

$y = \frac{38}{25}$

Step 4.2.1.1.4

Cancel the common factor of $2$ .

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Step 4.2.1.1.4.1

Factor $2$ out of $114$ .

$x = \frac{2 (57)}{25} \cdot \frac{1}{2} + 1$

$y = \frac{38}{25}$

Step 4.2.1.1.4.2

Cancel the common factor.

$x = \frac{2 \cdot 57}{25} \cdot \frac{1}{2} + 1$

$y = \frac{38}{25}$

Step 4.2.1.1.4.3

Rewrite the expression.

$x = \frac{57}{25} + 1$

$y = \frac{38}{25}$

$x = \frac{57}{25} + 1$

$y = \frac{38}{25}$

$x = \frac{57}{25} + 1$

$y = \frac{38}{25}$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Write $1$ as a fraction with a common denominator.

$x = \frac{57}{25} + \frac{25}{25}$

$y = \frac{38}{25}$

Step 4.2.1.2.2

Combine the numerators over the common denominator.

$x = \frac{57 + 25}{25}$

$y = \frac{38}{25}$

Step 4.2.1.2.3

Add $57$ and $25$ .

$x = \frac{82}{25}$

$y = \frac{38}{25}$

$x = \frac{82}{25}$

$y = \frac{38}{25}$

$x = \frac{82}{25}$

$y = \frac{38}{25}$

$x = \frac{82}{25}$

$y = \frac{38}{25}$

$x = \frac{82}{25}$

$y = \frac{38}{25}$

Step 5

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

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Step 5.1

Replace all occurrences of $y$ in $x = \frac{3 y}{2} + 1$ with $- 2$ .

$x = \frac{3 (- 2)}{2} + 1$

$y = - 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3 (- 2)}{2} + 1$ .

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Step 5.2.1.1

Multiply $3$ by $- 2$ .

$x = \frac{- 6}{2} + 1$

$y = - 2$

Step 5.2.1.2

Divide $- 6$ by $2$ .

$x = - 3 + 1$

$y = - 2$

Step 5.2.1.3

Add $- 3$ and $1$ .

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

Step 6

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

$(\frac{82}{25}, \frac{38}{25})$

$(- 2, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(\frac{82}{25}, \frac{38}{25}), (- 2, - 2)$

Equation Form:

$x = \frac{82}{25}, y = \frac{38}{25}$

$x = - 2, y = - 2$

Step 8