Algebra Examples

$x^{2} + y^{2} = 25$ $2 x - y = 5$

Step 1

Solve for $x$ in $2 x - y = 5$ .

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Step 1.1

Add $y$ to both sides of the equation.

$2 x = 5 + y$

$x^{2} + y^{2} = 25$

Step 1.2

Divide each term in $2 x = 5 + y$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = 5 + y$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2} + \frac{y}{2}$

$x^{2} + y^{2} = 25$

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.

$\frac{2 x}{2} = \frac{5}{2} + \frac{y}{2}$

$x^{2} + y^{2} = 25$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{2} + \frac{y}{2}$

$x^{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$x^{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$x^{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$x^{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$x^{2} + y^{2} = 25$

Step 2

Replace all occurrences of $x$ with $\frac{5}{2} + \frac{y}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x^{2} + y^{2} = 25$ with $\frac{5}{2} + \frac{y}{2}$ .

${(\frac{5}{2} + \frac{y}{2})}^{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Rewrite ${(\frac{5}{2} + \frac{y}{2})}^{2}$ as $(\frac{5}{2} + \frac{y}{2}) (\frac{5}{2} + \frac{y}{2})$ .

$(\frac{5}{2} + \frac{y}{2}) (\frac{5}{2} + \frac{y}{2}) + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.2

Expand $(\frac{5}{2} + \frac{y}{2}) (\frac{5}{2} + \frac{y}{2})$ using the FOIL Method.

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Step 2.2.1.1.2.1

Apply the distributive property.

$\frac{5}{2} \cdot (\frac{5}{2} + \frac{y}{2}) + \frac{y}{2} \cdot (\frac{5}{2} + \frac{y}{2}) + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.2.2

Apply the distributive property.

$\frac{5}{2} \cdot \frac{5}{2} + \frac{5}{2} \cdot \frac{y}{2} + \frac{y}{2} \cdot (\frac{5}{2} + \frac{y}{2}) + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.2.3

Apply the distributive property.

$\frac{5}{2} \cdot \frac{5}{2} + \frac{5}{2} \cdot \frac{y}{2} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5}{2} \cdot \frac{5}{2} + \frac{5}{2} \cdot \frac{y}{2} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

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 $\frac{5}{2} \cdot \frac{5}{2}$ .

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Step 2.2.1.1.3.1.1.1

Multiply $\frac{5}{2}$ by $\frac{5}{2}$ .

$\frac{5 \cdot 5}{2 \cdot 2} + \frac{5}{2} \cdot \frac{y}{2} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.1.2

Multiply $5$ by $5$ .

$\frac{25}{2 \cdot 2} + \frac{5}{2} \cdot \frac{y}{2} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.1.3

Multiply $2$ by $2$ .

$\frac{25}{4} + \frac{5}{2} \cdot \frac{y}{2} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + \frac{5}{2} \cdot \frac{y}{2} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.2

Multiply $\frac{5}{2} \cdot \frac{y}{2}$ .

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Step 2.2.1.1.3.1.2.1

Multiply $\frac{5}{2}$ by $\frac{y}{2}$ .

$\frac{25}{4} + \frac{5 y}{2 \cdot 2} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.2.2

Multiply $2$ by $2$ .

$\frac{25}{4} + \frac{5 y}{4} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + \frac{5 y}{4} + \frac{y}{2} \cdot \frac{5}{2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.3

Multiply $\frac{y}{2} \cdot \frac{5}{2}$ .

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Step 2.2.1.1.3.1.3.1

Multiply $\frac{y}{2}$ by $\frac{5}{2}$ .

$\frac{25}{4} + \frac{5 y}{4} + \frac{y \cdot 5}{2 \cdot 2} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.3.2

Multiply $2$ by $2$ .

$\frac{25}{4} + \frac{5 y}{4} + \frac{y \cdot 5}{4} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + \frac{5 y}{4} + \frac{y \cdot 5}{4} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.4

Move $5$ to the left of $y$ .

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 \cdot y}{4} + \frac{y}{2} \cdot \frac{y}{2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.5

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

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Step 2.2.1.1.3.1.5.1

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

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y \cdot y}{2 \cdot 2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.5.2

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

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y \cdot y}{2 \cdot 2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.5.3

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

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y \cdot y}{2 \cdot 2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.5.4

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

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y^{1 + 1}}{2 \cdot 2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.5.5

Add $1$ and $1$ .

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y^{2}}{2 \cdot 2} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.1.5.6

Multiply $2$ by $2$ .

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + \frac{5 y}{4} + \frac{5 y}{4} + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.3.2

Add $\frac{5 y}{4}$ and $\frac{5 y}{4}$ .

$\frac{25}{4} + 2 (\frac{5 y}{4}) + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + 2 (\frac{5 y}{4}) + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.4

Cancel the common factor of $2$ .

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Step 2.2.1.1.4.1

Factor $2$ out of $4$ .

$\frac{25}{4} + 2 (\frac{5 y}{2 (2)}) + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.4.2

Cancel the common factor.

$\frac{25}{4} + 2 (\frac{5 y}{2 \cdot 2}) + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.1.4.3

Rewrite the expression.

$\frac{25}{4} + \frac{5 y}{2} + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + \frac{5 y}{2} + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25}{4} + \frac{5 y}{2} + \frac{y^{2}}{4} + y^{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.2

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

$\frac{25}{4} + \frac{5 y}{2} + \frac{y^{2}}{4} + y^{2} \cdot \frac{4}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

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

$\frac{25}{4} + \frac{5 y}{2} + \frac{y^{2}}{4} + \frac{y^{2} \cdot 4}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$\frac{25}{4} + \frac{5 y}{2} + \frac{y^{2} + y^{2} \cdot 4}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.3.3

Combine the numerators over the common denominator.

$\frac{25 + y^{2} + y^{2} \cdot 4}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{25 + y^{2} + y^{2} \cdot 4}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.4

Move $4$ to the left of $y^{2}$ .

$\frac{25 + y^{2} + 4 y^{2}}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.5

Simplify terms.

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Step 2.2.1.5.1

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

$\frac{25 + 5 y^{2}}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.5.2

Factor $5$ out of $25 + 5 y^{2}$ .

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Step 2.2.1.5.2.1

Factor $5$ out of $25$ .

$\frac{5 \cdot 5 + 5 y^{2}}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.5.2.2

Factor $5$ out of $5 \cdot 5 + 5 y^{2}$ .

$\frac{5 (5 + y^{2})}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (5 + y^{2})}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (5 + y^{2})}{4} + \frac{5 y}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.6

To write $\frac{5 y}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 (5 + y^{2})}{4} + \frac{5 y}{2} \cdot \frac{2}{2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.7

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.7.1

Multiply $\frac{5 y}{2}$ by $\frac{2}{2}$ .

$\frac{5 (5 + y^{2})}{4} + \frac{5 y \cdot 2}{2 \cdot 2} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.7.2

Multiply $2$ by $2$ .

$\frac{5 (5 + y^{2})}{4} + \frac{5 y \cdot 2}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (5 + y^{2})}{4} + \frac{5 y \cdot 2}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.8

Combine the numerators over the common denominator.

$\frac{5 (5 + y^{2}) + 5 y \cdot 2}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.9

Simplify the numerator.

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Step 2.2.1.9.1

Factor $5$ out of $5 (5 + y^{2}) + 5 y \cdot 2$ .

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Step 2.2.1.9.1.1

Factor $5$ out of $5 y \cdot 2$ .

$\frac{5 (5 + y^{2}) + 5 (y \cdot 2)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.9.1.2

Factor $5$ out of $5 (5 + y^{2}) + 5 (y \cdot 2)$ .

$\frac{5 (5 + y^{2} + y \cdot 2)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (5 + y^{2} + y \cdot 2)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.9.2

Move $2$ to the left of $y$ .

$\frac{5 (5 + y^{2} + 2 \cdot y)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 2.2.1.9.3

Reorder terms.

$\frac{5 (y^{2} + 2 y + 5)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (y^{2} + 2 y + 5)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (y^{2} + 2 y + 5)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (y^{2} + 2 y + 5)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

$\frac{5 (y^{2} + 2 y + 5)}{4} = 25$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3

Solve for $y$ in $\frac{5 (y^{2} + 2 y + 5)}{4} = 25$ .

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Step 3.1

Multiply both sides by $4$ .

$\frac{5 (y^{2} + 2 y + 5)}{4} \cdot 4 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

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

Simplify $\frac{5 (y^{2} + 2 y + 5)}{4} \cdot 4$ .

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Step 3.2.1.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{5 (y^{2} + 2 y + 5)}{4} \cdot 4 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.2.1.1.1.2

Rewrite the expression.

$5 (y^{2} + 2 y + 5) = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

$5 (y^{2} + 2 y + 5) = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.2.1.1.2

Apply the distributive property.

$5 y^{2} + 5 (2 y) + 5 \cdot 5 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.2.1.1.3

Simplify.

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Step 3.2.1.1.3.1

Multiply $2$ by $5$ .

$5 y^{2} + 10 y + 5 \cdot 5 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.2.1.1.3.2

Multiply $5$ by $5$ .

$5 y^{2} + 10 y + 25 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

$5 y^{2} + 10 y + 25 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

$5 y^{2} + 10 y + 25 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

$5 y^{2} + 10 y + 25 = 25 \cdot 4$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $25$ by $4$ .

$5 y^{2} + 10 y + 25 = 100$

$x = \frac{5}{2} + \frac{y}{2}$

$5 y^{2} + 10 y + 25 = 100$

$x = \frac{5}{2} + \frac{y}{2}$

$5 y^{2} + 10 y + 25 = 100$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3

Solve for $y$ .

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Step 3.3.1

Subtract $100$ from both sides of the equation.

$5 y^{2} + 10 y + 25 - 100 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.2

Subtract $100$ from $25$ .

$5 y^{2} + 10 y - 75 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3

Factor the left side of the equation.

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Step 3.3.3.1

Factor $5$ out of $5 y^{2} + 10 y - 75$ .

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Step 3.3.3.1.1

Factor $5$ out of $5 y^{2}$ .

$5 (y^{2}) + 10 y - 75 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3.1.2

Factor $5$ out of $10 y$ .

$5 (y^{2}) + 5 (2 y) - 75 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3.1.3

Factor $5$ out of $- 75$ .

$5 y^{2} + 5 (2 y) + 5 \cdot - 15 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3.1.4

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

$5 (y^{2} + 2 y) + 5 \cdot - 15 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3.1.5

Factor $5$ out of $5 (y^{2} + 2 y) + 5 \cdot - 15$ .

$5 (y^{2} + 2 y - 15) = 0$

$x = \frac{5}{2} + \frac{y}{2}$

$5 (y^{2} + 2 y - 15) = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3.2

Factor.

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Step 3.3.3.2.1

Factor $y^{2} + 2 y - 15$ using the AC method.

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Step 3.3.3.2.1.1

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 $- 15$ and whose sum is $2$ .

$- 3, 5$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3.2.1.2

Write the factored form using these integers.

$5 ((y - 3) (y + 5)) = 0$

$x = \frac{5}{2} + \frac{y}{2}$

$5 ((y - 3) (y + 5)) = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.3.2.2

Remove unnecessary parentheses.

$5 (y - 3) (y + 5) = 0$

$x = \frac{5}{2} + \frac{y}{2}$

$5 (y - 3) (y + 5) = 0$

$x = \frac{5}{2} + \frac{y}{2}$

$5 (y - 3) (y + 5) = 0$

$x = \frac{5}{2} + \frac{y}{2}$

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 $0$ .

$y - 3 = 0$

$y + 5 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.5

Set $y - 3$ equal to $0$ and solve for $y$ .

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Step 3.3.5.1

Set $y - 3$ equal to $0$ .

$y - 3 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.5.2

Add $3$ to both sides of the equation.

$y = 3$

$x = \frac{5}{2} + \frac{y}{2}$

$y = 3$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.6

Set $y + 5$ equal to $0$ and solve for $y$ .

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Step 3.3.6.1

Set $y + 5$ equal to $0$ .

$y + 5 = 0$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.6.2

Subtract $5$ from both sides of the equation.

$y = - 5$

$x = \frac{5}{2} + \frac{y}{2}$

$y = - 5$

$x = \frac{5}{2} + \frac{y}{2}$

Step 3.3.7

The final solution is all the values that make $5 (y - 3) (y + 5) = 0$ true.

$y = 3, - 5$

$x = \frac{5}{2} + \frac{y}{2}$

$y = 3, - 5$

$x = \frac{5}{2} + \frac{y}{2}$

$y = 3, - 5$

$x = \frac{5}{2} + \frac{y}{2}$

Step 4

Replace all occurrences of $y$ with $3$ in each equation.

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Step 4.1

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

$x = \frac{5}{2} + \frac{3}{2}$

$y = 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{5}{2} + \frac{3}{2}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{5 + 3}{2}$

$y = 3$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Add $5$ and $3$ .

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

$y = 3$

Step 4.2.1.2.2

Divide $8$ by $2$ .

$x = 4$

$y = 3$

$x = 4$

$y = 3$

$x = 4$

$y = 3$

$x = 4$

$y = 3$

$x = 4$

$y = 3$

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 $x = \frac{5}{2} + \frac{y}{2}$ with $- 5$ .

$x = \frac{5}{2} + \frac{- 5}{2}$

$y = - 5$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{2} + \frac{- 5}{2}$ .

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Step 5.2.1.1

Combine the numerators over the common denominator.

$x = \frac{5 - 5}{2}$

$y = - 5$

Step 5.2.1.2

Simplify the expression.

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Step 5.2.1.2.1

Subtract $5$ from $5$ .

$x = \frac{0}{2}$

$y = - 5$

Step 5.2.1.2.2

Divide $0$ by $2$ .

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

Step 6

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

$(4, 3)$

$(0, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 3), (0, - 5)$

Equation Form:

$x = 4, y = 3$

$x = 0, y = - 5$

Step 8