Algebra Examples

$x^{2} + y^{2} = 16$ $3 x - 4 y = 20$

Step 1

Solve for $x$ in $3 x - 4 y = 20$ .

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Step 1.1

Add $4 y$ to both sides of the equation.

$3 x = 20 + 4 y$

$x^{2} + y^{2} = 16$

Step 1.2

Divide each term in $3 x = 20 + 4 y$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x = 20 + 4 y$ by $3$ .

$\frac{3 x}{3} = \frac{20}{3} + \frac{4 y}{3}$

$x^{2} + y^{2} = 16$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{20}{3} + \frac{4 y}{3}$

$x^{2} + y^{2} = 16$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{3} + \frac{4 y}{3}$

$x^{2} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$x^{2} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$x^{2} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$x^{2} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$x^{2} + y^{2} = 16$

Step 2

Replace all occurrences of $x$ with $\frac{20}{3} + \frac{4 y}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x^{2} + y^{2} = 16$ with $\frac{20}{3} + \frac{4 y}{3}$ .

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

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${(\frac{20}{3} + \frac{4 y}{3})}^{2} + y^{2}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Rewrite ${(\frac{20}{3} + \frac{4 y}{3})}^{2}$ as $(\frac{20}{3} + \frac{4 y}{3}) (\frac{20}{3} + \frac{4 y}{3})$ .

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

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.2

Expand $(\frac{20}{3} + \frac{4 y}{3}) (\frac{20}{3} + \frac{4 y}{3})$ using the FOIL Method.

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Step 2.2.1.1.2.1

Apply the distributive property.

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

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.2.2

Apply the distributive property.

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

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.2.3

Apply the distributive property.

$\frac{20}{3} \cdot \frac{20}{3} + \frac{20}{3} \cdot \frac{4 y}{3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{20}{3} \cdot \frac{20}{3} + \frac{20}{3} \cdot \frac{4 y}{3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

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 $\frac{20}{3} \cdot \frac{20}{3}$ .

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Step 2.2.1.1.3.1.1.1

Multiply $\frac{20}{3}$ by $\frac{20}{3}$ .

$\frac{20 \cdot 20}{3 \cdot 3} + \frac{20}{3} \cdot \frac{4 y}{3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.1.2

Multiply $20$ by $20$ .

$\frac{400}{3 \cdot 3} + \frac{20}{3} \cdot \frac{4 y}{3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.1.3

Multiply $3$ by $3$ .

$\frac{400}{9} + \frac{20}{3} \cdot \frac{4 y}{3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + \frac{20}{3} \cdot \frac{4 y}{3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.2

Multiply $\frac{20}{3} \cdot \frac{4 y}{3}$ .

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Step 2.2.1.1.3.1.2.1

Multiply $\frac{20}{3}$ by $\frac{4 y}{3}$ .

$\frac{400}{9} + \frac{20 (4 y)}{3 \cdot 3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.2.2

Multiply $4$ by $20$ .

$\frac{400}{9} + \frac{80 y}{3 \cdot 3} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.2.3

Multiply $3$ by $3$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + \frac{80 y}{9} + \frac{4 y}{3} \cdot \frac{20}{3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.3

Multiply $\frac{4 y}{3} \cdot \frac{20}{3}$ .

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Step 2.2.1.1.3.1.3.1

Multiply $\frac{4 y}{3}$ by $\frac{20}{3}$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{4 y \cdot 20}{3 \cdot 3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.3.2

Multiply $20$ by $4$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{3 \cdot 3} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.3.3

Multiply $3$ by $3$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{4 y}{3} \cdot \frac{4 y}{3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.4

Multiply $\frac{4 y}{3} \cdot \frac{4 y}{3}$ .

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Step 2.2.1.1.3.1.4.1

Multiply $\frac{4 y}{3}$ by $\frac{4 y}{3}$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{4 y (4 y)}{3 \cdot 3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.4.2

Multiply $4$ by $4$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 y \cdot y}{3 \cdot 3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.4.3

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

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 (y \cdot y)}{3 \cdot 3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.4.4

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

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 (y \cdot y)}{3 \cdot 3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.4.5

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

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 y^{1 + 1}}{3 \cdot 3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.4.6

Add $1$ and $1$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 y^{2}}{3 \cdot 3} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.1.4.7

Multiply $3$ by $3$ .

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + \frac{80 y}{9} + \frac{80 y}{9} + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.3.2

Add $\frac{80 y}{9}$ and $\frac{80 y}{9}$ .

$\frac{400}{9} + 2 (\frac{80 y}{9}) + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + 2 (\frac{80 y}{9}) + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.4

Multiply $2 \frac{80 y}{9}$ .

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Step 2.2.1.1.4.1

Combine $2$ and $\frac{80 y}{9}$ .

$\frac{400}{9} + \frac{2 (80 y)}{9} + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.1.4.2

Multiply $80$ by $2$ .

$\frac{400}{9} + \frac{160 y}{9} + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + \frac{160 y}{9} + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400}{9} + \frac{160 y}{9} + \frac{16 y^{2}}{9} + y^{2} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.2

To write $y^{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{400}{9} + \frac{160 y}{9} + \frac{16 y^{2}}{9} + y^{2} \cdot \frac{9}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $y^{2}$ and $\frac{9}{9}$ .

$\frac{400}{9} + \frac{160 y}{9} + \frac{16 y^{2}}{9} + \frac{y^{2} \cdot 9}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$\frac{400}{9} + \frac{160 y}{9} + \frac{16 y^{2} + y^{2} \cdot 9}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.3.3

Combine the numerators over the common denominator.

$\frac{400 + 160 y + 16 y^{2} + y^{2} \cdot 9}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{400 + 160 y + 16 y^{2} + y^{2} \cdot 9}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.4

Move $9$ to the left of $y^{2}$ .

$\frac{400 + 160 y + 16 y^{2} + 9 y^{2}}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.5

Simplify terms.

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Step 2.2.1.5.1

Add $16 y^{2}$ and $9 y^{2}$ .

$\frac{400 + 160 y + 25 y^{2}}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.5.2

Factor $5$ out of $400 + 160 y + 25 y^{2}$ .

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Step 2.2.1.5.2.1

Factor $5$ out of $400$ .

$\frac{5 (80) + 160 y + 25 y^{2}}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.5.2.2

Factor $5$ out of $160 y$ .

$\frac{5 (80) + 5 (32 y) + 25 y^{2}}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.5.2.3

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

$\frac{5 (80) + 5 (32 y) + 5 (5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.5.2.4

Factor $5$ out of $5 (80) + 5 (32 y)$ .

$\frac{5 (80 + 32 y) + 5 (5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 2.2.1.5.2.5

Factor $5$ out of $5 (80 + 32 y) + 5 (5 y^{2})$ .

$\frac{5 (80 + 32 y + 5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{5 (80 + 32 y + 5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{5 (80 + 32 y + 5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{5 (80 + 32 y + 5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{5 (80 + 32 y + 5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

$\frac{5 (80 + 32 y + 5 y^{2})}{9} = 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3

Solve for $y$ in $\frac{5 (80 + 32 y + 5 y^{2})}{9} = 16$ .

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Step 3.1

Multiply both sides by $9$ .

$\frac{5 (80 + 32 y + 5 y^{2})}{9} \cdot 9 = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

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 $\frac{5 (80 + 32 y + 5 y^{2})}{9} \cdot 9$ .

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Step 3.2.1.1.1

Cancel the common factor of $9$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{5 (80 + 32 y + 5 y^{2})}{9} \cdot 9 = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.1.1.1.2

Rewrite the expression.

$5 (80 + 32 y + 5 y^{2}) = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

$5 (80 + 32 y + 5 y^{2}) = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.1.1.2

Apply the distributive property.

$5 \cdot 80 + 5 (32 y) + 5 (5 y^{2}) = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.1.1.3

Simplify.

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Step 3.2.1.1.3.1

Multiply $5$ by $80$ .

$400 + 5 (32 y) + 5 (5 y^{2}) = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.1.1.3.2

Multiply $32$ by $5$ .

$400 + 160 y + 5 (5 y^{2}) = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.1.1.3.3

Multiply $5$ by $5$ .

$400 + 160 y + 25 y^{2} = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

$400 + 160 y + 25 y^{2} = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.1.1.4

Move $400$ .

$160 y + 25 y^{2} + 400 = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.1.1.5

Reorder $160 y$ and $25 y^{2}$ .

$25 y^{2} + 160 y + 400 = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

$25 y^{2} + 160 y + 400 = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

$25 y^{2} + 160 y + 400 = 16 \cdot 9$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $16$ by $9$ .

$25 y^{2} + 160 y + 400 = 144$

$x = \frac{20}{3} + \frac{4 y}{3}$

$25 y^{2} + 160 y + 400 = 144$

$x = \frac{20}{3} + \frac{4 y}{3}$

$25 y^{2} + 160 y + 400 = 144$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3

Solve for $y$ .

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Step 3.3.1

Subtract $144$ from both sides of the equation.

$25 y^{2} + 160 y + 400 - 144 = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.2

Subtract $144$ from $400$ .

$25 y^{2} + 160 y + 256 = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.3

Factor using the perfect square rule.

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Step 3.3.3.1

Rewrite $25 y^{2}$ as ${(5 y)}^{2}$ .

${(5 y)}^{2} + 160 y + 256 = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.3.2

Rewrite $256$ as $16^{2}$ .

${(5 y)}^{2} + 160 y + 16^{2} = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.3.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$160 y = 2 \cdot (5 y) \cdot 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.3.4

Rewrite the polynomial.

${(5 y)}^{2} + 2 \cdot (5 y) \cdot 16 + 16^{2} = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.3.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5 y$ and $b = 16$ .

${(5 y + 16)}^{2} = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

${(5 y + 16)}^{2} = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.4

Set the $5 y + 16$ equal to $0$ .

$5 y + 16 = 0$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.5

Solve for $y$ .

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Step 3.3.5.1

Subtract $16$ from both sides of the equation.

$5 y = - 16$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.5.2

Divide each term in $5 y = - 16$ by $5$ and simplify.

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Step 3.3.5.2.1

Divide each term in $5 y = - 16$ by $5$ .

$\frac{5 y}{5} = \frac{- 16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.5.2.2

Simplify the left side.

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Step 3.3.5.2.2.1

Cancel the common factor of $5$ .

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Step 3.3.5.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.5.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

$y = \frac{- 16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

$y = \frac{- 16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 3.3.5.2.3

Simplify the right side.

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Step 3.3.5.2.3.1

Move the negative in front of the fraction.

$y = - \frac{16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

$y = - \frac{16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

$y = - \frac{16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

$y = - \frac{16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

$y = - \frac{16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

$y = - \frac{16}{5}$

$x = \frac{20}{3} + \frac{4 y}{3}$

Step 4

Replace all occurrences of $y$ with $- \frac{16}{5}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{20}{3} + \frac{4 y}{3}$ with $- \frac{16}{5}$ .

$x = \frac{20}{3} + \frac{4 (- \frac{16}{5})}{3}$

$y = - \frac{16}{5}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{20}{3} + \frac{4 (- \frac{16}{5})}{3}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{20 + 4 (- \frac{16}{5})}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.2

Simplify each term.

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Step 4.2.1.2.1

Multiply $4 (- \frac{16}{5})$ .

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Step 4.2.1.2.1.1

Multiply $- 1$ by $4$ .

$x = \frac{20 - 4 (\frac{16}{5})}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.2.1.2

Combine $- 4$ and $\frac{16}{5}$ .

$x = \frac{20 + \frac{- 4 \cdot 16}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.2.1.3

Multiply $- 4$ by $16$ .

$x = \frac{20 + \frac{- 64}{5}}{3}$

$y = - \frac{16}{5}$

$x = \frac{20 + \frac{- 64}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.2.2

Move the negative in front of the fraction.

$x = \frac{20 - \frac{64}{5}}{3}$

$y = - \frac{16}{5}$

$x = \frac{20 - \frac{64}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.3

To write $20$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \frac{20 \cdot \frac{5}{5} - \frac{64}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.4

Combine $20$ and $\frac{5}{5}$ .

$x = \frac{\frac{20 \cdot 5}{5} - \frac{64}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.5

Combine the numerators over the common denominator.

$x = \frac{\frac{20 \cdot 5 - 64}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.6

Simplify the numerator.

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Step 4.2.1.6.1

Multiply $20$ by $5$ .

$x = \frac{\frac{100 - 64}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.6.2

Subtract $64$ from $100$ .

$x = \frac{\frac{36}{5}}{3}$

$y = - \frac{16}{5}$

$x = \frac{\frac{36}{5}}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.7

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{36}{5} \cdot \frac{1}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.8

Cancel the common factor of $3$ .

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Step 4.2.1.8.1

Factor $3$ out of $36$ .

$x = \frac{3 (12)}{5} \cdot \frac{1}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.8.2

Cancel the common factor.

$x = \frac{3 \cdot 12}{5} \cdot \frac{1}{3}$

$y = - \frac{16}{5}$

Step 4.2.1.8.3

Rewrite the expression.

$x = \frac{12}{5}$

$y = - \frac{16}{5}$

$x = \frac{12}{5}$

$y = - \frac{16}{5}$

$x = \frac{12}{5}$

$y = - \frac{16}{5}$

$x = \frac{12}{5}$

$y = - \frac{16}{5}$

$x = \frac{12}{5}$

$y = - \frac{16}{5}$

Step 5

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

$(\frac{12}{5}, - \frac{16}{5})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{12}{5}, - \frac{16}{5})$

Equation Form:

$x = \frac{12}{5}, y = - \frac{16}{5}$

Step 7