Algebra Examples

$- \frac{5}{9} x + \frac{7}{6} y = - \frac{62}{9}$ $- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1

Solve for $x$ in $- \frac{5}{9} x + \frac{7}{6} y = - \frac{62}{9}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{5}{9}$ .

$- \frac{x \cdot 5}{9} + \frac{7}{6} y = - \frac{62}{9}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.1.2

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

$- \frac{5 \cdot x}{9} + \frac{7}{6} y = - \frac{62}{9}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.1.3

Combine $\frac{7}{6}$ and $y$ .

$- \frac{5 x}{9} + \frac{7 y}{6} = - \frac{62}{9}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$- \frac{5 x}{9} + \frac{7 y}{6} = - \frac{62}{9}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.2

Subtract $\frac{7 y}{6}$ from both sides of the equation.

$- \frac{5 x}{9} = - \frac{62}{9} - \frac{7 y}{6}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.3

Multiply both sides of the equation by $- \frac{9}{5}$ .

$- \frac{9}{5} \cdot (- \frac{5 x}{9}) = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Simplify $- \frac{9}{5} (- \frac{5 x}{9})$ .

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Step 1.4.1.1.1

Cancel the common factor of $9$ .

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Step 1.4.1.1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- 9}{5} \cdot (- \frac{5 x}{9}) = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.1.2

Move the leading negative in $- \frac{5 x}{9}$ into the numerator.

$\frac{- 9}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.1.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.1.4

Cancel the common factor.

$\frac{9 \cdot - 1}{5} \cdot \frac{- 5 x}{9} = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} \cdot (- 5 x) = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$\frac{- 1}{5} \cdot (- 5 x) = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.2

Cancel the common factor of $5$ .

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Step 1.4.1.1.2.1

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} \cdot (5 (- x)) = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} \cdot (5 (- x)) = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.2.3

Rewrite the expression.

$x = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.3

Multiply.

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Step 1.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = - \frac{9}{5} \cdot (- \frac{62}{9} - \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $- \frac{9}{5} (- \frac{62}{9} - \frac{7 y}{6})$ .

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Step 1.4.2.1.1

Apply the distributive property.

$x = - \frac{9}{5} \cdot (- \frac{62}{9}) - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.2

Cancel the common factor of $9$ .

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Step 1.4.2.1.2.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$x = \frac{- 9}{5} \cdot (- \frac{62}{9}) - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.2.2

Move the leading negative in $- \frac{62}{9}$ into the numerator.

$x = \frac{- 9}{5} \cdot \frac{- 62}{9} - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.2.3

Factor $9$ out of $- 9$ .

$x = \frac{9 (- 1)}{5} \cdot \frac{- 62}{9} - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.2.4

Cancel the common factor.

$x = \frac{9 \cdot - 1}{5} \cdot \frac{- 62}{9} - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.2.5

Rewrite the expression.

$x = \frac{- 1}{5} \cdot - 62 - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{- 1}{5} \cdot - 62 - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.3

Combine $\frac{- 1}{5}$ and $- 62$ .

$x = \frac{62}{5} - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.4

Multiply $- 1$ by $- 62$ .

$x = \frac{62}{5} - \frac{9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.5

Cancel the common factor of $3$ .

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Step 1.4.2.1.5.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$x = \frac{62}{5} + \frac{- 9}{5} \cdot (- \frac{7 y}{6})$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.5.2

Move the leading negative in $- \frac{7 y}{6}$ into the numerator.

$x = \frac{62}{5} + \frac{- 9}{5} \cdot \frac{- 7 y}{6}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.5.3

Factor $3$ out of $- 9$ .

$x = \frac{62}{5} + \frac{3 (- 3)}{5} \cdot \frac{- 7 y}{6}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.5.4

Factor $3$ out of $6$ .

$x = \frac{62}{5} + \frac{3 \cdot - 3}{5} \cdot \frac{- 7 y}{3 \cdot 2}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.5.5

Cancel the common factor.

$x = \frac{62}{5} + \frac{3 \cdot - 3}{5} \cdot \frac{- 7 y}{3 \cdot 2}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.5.6

Rewrite the expression.

$x = \frac{62}{5} + \frac{- 3}{5} \cdot \frac{- 7 y}{2}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{62}{5} + \frac{- 3}{5} \cdot \frac{- 7 y}{2}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.6

Multiply $\frac{- 3}{5}$ by $\frac{- 7 y}{2}$ .

$x = \frac{62}{5} + \frac{- 3 (- 7 y)}{5 \cdot 2}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.7

Multiply.

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Step 1.4.2.1.7.1

Multiply $- 7$ by $- 3$ .

$x = \frac{62}{5} + \frac{21 y}{5 \cdot 2}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.4.2.1.7.2

Multiply $5$ by $2$ .

$x = \frac{62}{5} + \frac{21 y}{10}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{62}{5} + \frac{21 y}{10}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{62}{5} + \frac{21 y}{10}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{62}{5} + \frac{21 y}{10}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{62}{5} + \frac{21 y}{10}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 1.5

Reorder $\frac{62}{5}$ and $\frac{21 y}{10}$ .

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$

Step 2

Replace all occurrences of $x$ with $\frac{21 y}{10} + \frac{62}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- \frac{8}{7} x - \frac{5}{6} y = - \frac{26}{21}$ with $\frac{21 y}{10} + \frac{62}{5}$ .

$- \frac{8}{7} \cdot (\frac{21 y}{10} + \frac{62}{5}) - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- \frac{8}{7} \cdot (\frac{21 y}{10} + \frac{62}{5}) - \frac{5}{6} y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$- \frac{8}{7} \cdot \frac{21 y}{10} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{8}{7}$ into the numerator.

$\frac{- 8}{7} \cdot \frac{21 y}{10} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.2.2

Factor $2$ out of $- 8$ .

$\frac{2 (- 4)}{7} \cdot \frac{21 y}{10} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.2.3

Factor $2$ out of $10$ .

$\frac{2 \cdot - 4}{7} \cdot \frac{21 y}{2 \cdot 5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.2.4

Cancel the common factor.

$\frac{2 \cdot - 4}{7} \cdot \frac{21 y}{2 \cdot 5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.2.5

Rewrite the expression.

$\frac{- 4}{7} \cdot \frac{21 y}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$\frac{- 4}{7} \cdot \frac{21 y}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.3

Cancel the common factor of $7$ .

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Step 2.2.1.1.3.1

Factor $7$ out of $21 y$ .

$\frac{- 4}{7} \cdot \frac{7 (3 y)}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.3.2

Cancel the common factor.

$\frac{- 4}{7} \cdot \frac{7 (3 y)}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.3.3

Rewrite the expression.

$- 4 \frac{3 y}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- 4 \frac{3 y}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.4

Combine $- 4$ and $\frac{3 y}{5}$ .

$\frac{- 4 (3 y)}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.5

Multiply $3$ by $- 4$ .

$\frac{- 12 y}{5} - \frac{8}{7} \cdot \frac{62}{5} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.6

Multiply $- \frac{8}{7} \cdot \frac{62}{5}$ .

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Step 2.2.1.1.6.1

Multiply $\frac{62}{5}$ by $\frac{8}{7}$ .

$\frac{- 12 y}{5} - \frac{62 \cdot 8}{5 \cdot 7} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.6.2

Multiply $62$ by $8$ .

$\frac{- 12 y}{5} - \frac{496}{5 \cdot 7} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.6.3

Multiply $5$ by $7$ .

$\frac{- 12 y}{5} - \frac{496}{35} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$\frac{- 12 y}{5} - \frac{496}{35} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.7

Move the negative in front of the fraction.

$- \frac{12 y}{5} - \frac{496}{35} - \frac{5}{6} y = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.8

Combine $y$ and $\frac{5}{6}$ .

$- \frac{12 y}{5} - \frac{496}{35} - \frac{y \cdot 5}{6} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.1.9

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

$- \frac{12 y}{5} - \frac{496}{35} - \frac{5 y}{6} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{12 y}{5} - \frac{496}{35} - \frac{5 y}{6} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.2

To write $- \frac{12 y}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{12 y}{5} \cdot \frac{6}{6} - \frac{5 y}{6} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.3

To write $- \frac{5 y}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{12 y}{5} \cdot \frac{6}{6} - \frac{5 y}{6} \cdot \frac{5}{5} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.4.1

Multiply $\frac{12 y}{5}$ by $\frac{6}{6}$ .

$- \frac{12 y \cdot 6}{5 \cdot 6} - \frac{5 y}{6} \cdot \frac{5}{5} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.4.2

Multiply $5$ by $6$ .

$- \frac{12 y \cdot 6}{30} - \frac{5 y}{6} \cdot \frac{5}{5} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.4.3

Multiply $\frac{5 y}{6}$ by $\frac{5}{5}$ .

$- \frac{12 y \cdot 6}{30} - \frac{5 y \cdot 5}{6 \cdot 5} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.4.4

Multiply $6$ by $5$ .

$- \frac{12 y \cdot 6}{30} - \frac{5 y \cdot 5}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{12 y \cdot 6}{30} - \frac{5 y \cdot 5}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.5

Combine the numerators over the common denominator.

$\frac{- 12 y \cdot 6 - 5 y \cdot 5}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6

Simplify each term.

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Step 2.2.1.6.1

Simplify the numerator.

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Step 2.2.1.6.1.1

Factor $y$ out of $- 12 y \cdot 6 - 5 y \cdot 5$ .

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Step 2.2.1.6.1.1.1

Factor $y$ out of $- 12 y \cdot 6$ .

$\frac{y (- 12 \cdot 6) - 5 y \cdot 5}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6.1.1.2

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

$\frac{y (- 12 \cdot 6) + y (- 5 \cdot 5)}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6.1.1.3

Factor $y$ out of $y (- 12 \cdot 6) + y (- 5 \cdot 5)$ .

$\frac{y (- 12 \cdot 6 - 5 \cdot 5)}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$\frac{y (- 12 \cdot 6 - 5 \cdot 5)}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6.1.2

Multiply $- 12$ by $6$ .

$\frac{y (- 72 - 5 \cdot 5)}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6.1.3

Multiply $- 5$ by $5$ .

$\frac{y (- 72 - 25)}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6.1.4

Subtract $25$ from $- 72$ .

$\frac{y \cdot - 97}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$\frac{y \cdot - 97}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6.2

Move $- 97$ to the left of $y$ .

$\frac{- 97 \cdot y}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 2.2.1.6.3

Move the negative in front of the fraction.

$- \frac{97 y}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} - \frac{496}{35} = - \frac{26}{21}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3

Solve for $y$ in $- \frac{97 y}{30} - \frac{496}{35} = - \frac{26}{21}$ .

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Step 3.1

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

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Step 3.1.1

Add $\frac{496}{35}$ to both sides of the equation.

$- \frac{97 y}{30} = - \frac{26}{21} + \frac{496}{35}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.2

To write $- \frac{26}{21}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{97 y}{30} = - \frac{26}{21} \cdot \frac{5}{5} + \frac{496}{35}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.3

To write $\frac{496}{35}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{97 y}{30} = - \frac{26}{21} \cdot \frac{5}{5} + \frac{496}{35} \cdot \frac{3}{3}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.4

Write each expression with a common denominator of $105$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.4.1

Multiply $\frac{26}{21}$ by $\frac{5}{5}$ .

$- \frac{97 y}{30} = - \frac{26 \cdot 5}{21 \cdot 5} + \frac{496}{35} \cdot \frac{3}{3}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.4.2

Multiply $21$ by $5$ .

$- \frac{97 y}{30} = - \frac{26 \cdot 5}{105} + \frac{496}{35} \cdot \frac{3}{3}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.4.3

Multiply $\frac{496}{35}$ by $\frac{3}{3}$ .

$- \frac{97 y}{30} = - \frac{26 \cdot 5}{105} + \frac{496 \cdot 3}{35 \cdot 3}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.4.4

Multiply $35$ by $3$ .

$- \frac{97 y}{30} = - \frac{26 \cdot 5}{105} + \frac{496 \cdot 3}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} = - \frac{26 \cdot 5}{105} + \frac{496 \cdot 3}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.5

Combine the numerators over the common denominator.

$- \frac{97 y}{30} = \frac{- 26 \cdot 5 + 496 \cdot 3}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.6

Simplify the numerator.

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Step 3.1.6.1

Multiply $- 26$ by $5$ .

$- \frac{97 y}{30} = \frac{- 130 + 496 \cdot 3}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.6.2

Multiply $496$ by $3$ .

$- \frac{97 y}{30} = \frac{- 130 + 1488}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.6.3

Add $- 130$ and $1488$ .

$- \frac{97 y}{30} = \frac{1358}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} = \frac{1358}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.7

Cancel the common factor of $1358$ and $105$ .

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Step 3.1.7.1

Factor $7$ out of $1358$ .

$- \frac{97 y}{30} = \frac{7 (194)}{105}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.7.2

Cancel the common factors.

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Step 3.1.7.2.1

Factor $7$ out of $105$ .

$- \frac{97 y}{30} = \frac{7 \cdot 194}{7 \cdot 15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.7.2.2

Cancel the common factor.

$- \frac{97 y}{30} = \frac{7 \cdot 194}{7 \cdot 15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.1.7.2.3

Rewrite the expression.

$- \frac{97 y}{30} = \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} = \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} = \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$- \frac{97 y}{30} = \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.2

Multiply both sides of the equation by $- \frac{30}{97}$ .

$- \frac{30}{97} \cdot (- \frac{97 y}{30}) = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $- \frac{30}{97} (- \frac{97 y}{30})$ .

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Step 3.3.1.1.1

Cancel the common factor of $30$ .

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Step 3.3.1.1.1.1

Move the leading negative in $- \frac{30}{97}$ into the numerator.

$\frac{- 30}{97} \cdot (- \frac{97 y}{30}) = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.1.2

Move the leading negative in $- \frac{97 y}{30}$ into the numerator.

$\frac{- 30}{97} \cdot \frac{- 97 y}{30} = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.1.3

Factor $30$ out of $- 30$ .

$\frac{30 (- 1)}{97} \cdot \frac{- 97 y}{30} = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.1.4

Cancel the common factor.

$\frac{30 \cdot - 1}{97} \cdot \frac{- 97 y}{30} = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{97} \cdot (- 97 y) = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$\frac{- 1}{97} \cdot (- 97 y) = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.2

Cancel the common factor of $97$ .

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Step 3.3.1.1.2.1

Factor $97$ out of $- 97 y$ .

$\frac{- 1}{97} \cdot (97 (- y)) = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{97} \cdot (97 (- y)) = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.3

Multiply.

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Step 3.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - \frac{30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $- \frac{30}{97} \cdot \frac{194}{15}$ .

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Step 3.3.2.1.1

Cancel the common factor of $15$ .

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Step 3.3.2.1.1.1

Move the leading negative in $- \frac{30}{97}$ into the numerator.

$y = \frac{- 30}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2.1.1.2

Factor $15$ out of $- 30$ .

$y = \frac{15 (- 2)}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2.1.1.3

Cancel the common factor.

$y = \frac{15 \cdot - 2}{97} \cdot \frac{194}{15}$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2.1.1.4

Rewrite the expression.

$y = \frac{- 2}{97} \cdot 194$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = \frac{- 2}{97} \cdot 194$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2.1.2

Cancel the common factor of $97$ .

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Step 3.3.2.1.2.1

Factor $97$ out of $194$ .

$y = \frac{- 2}{97} \cdot (97 (2))$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2.1.2.2

Cancel the common factor.

$y = \frac{- 2}{97} \cdot (97 \cdot 2)$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2.1.2.3

Rewrite the expression.

$y = - 2 \cdot 2$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - 2 \cdot 2$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 3.3.2.1.3

Multiply $- 2$ by $2$ .

$y = - 4$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - 4$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - 4$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - 4$

$x = \frac{21 y}{10} + \frac{62}{5}$

$y = - 4$

$x = \frac{21 y}{10} + \frac{62}{5}$

Step 4

Replace all occurrences of $y$ with $- 4$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{21 y}{10} + \frac{62}{5}$ with $- 4$ .

$x = \frac{21 (- 4)}{10} + \frac{62}{5}$

$y = - 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{21 (- 4)}{10} + \frac{62}{5}$ .

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Step 4.2.1.1

Multiply $21$ by $- 4$ .

$x = \frac{- 84}{10} + \frac{62}{5}$

$y = - 4$

Step 4.2.1.2

Simplify each term.

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Step 4.2.1.2.1

Cancel the common factor of $- 84$ and $10$ .

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Step 4.2.1.2.1.1

Factor $2$ out of $- 84$ .

$x = \frac{2 (- 42)}{10} + \frac{62}{5}$

$y = - 4$

Step 4.2.1.2.1.2

Cancel the common factors.

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Step 4.2.1.2.1.2.1

Factor $2$ out of $10$ .

$x = \frac{2 \cdot - 42}{2 \cdot 5} + \frac{62}{5}$

$y = - 4$

Step 4.2.1.2.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot - 42}{2 \cdot 5} + \frac{62}{5}$

$y = - 4$

Step 4.2.1.2.1.2.3

Rewrite the expression.

$x = \frac{- 42}{5} + \frac{62}{5}$

$y = - 4$

$x = \frac{- 42}{5} + \frac{62}{5}$

$y = - 4$

$x = \frac{- 42}{5} + \frac{62}{5}$

$y = - 4$

Step 4.2.1.2.2

Move the negative in front of the fraction.

$x = - \frac{42}{5} + \frac{62}{5}$

$y = - 4$

$x = - \frac{42}{5} + \frac{62}{5}$

$y = - 4$

Step 4.2.1.3

Combine fractions.

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Step 4.2.1.3.1

Combine the numerators over the common denominator.

$x = \frac{- 42 + 62}{5}$

$y = - 4$

Step 4.2.1.3.2

Simplify the expression.

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Step 4.2.1.3.2.1

Add $- 42$ and $62$ .

$x = \frac{20}{5}$

$y = - 4$

Step 4.2.1.3.2.2

Divide $20$ by $5$ .

$x = 4$

$y = - 4$

$x = 4$

$y = - 4$

$x = 4$

$y = - 4$

$x = 4$

$y = - 4$

$x = 4$

$y = - 4$

$x = 4$

$y = - 4$

Step 5

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

$(4, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 4)$

Equation Form:

$x = 4, y = - 4$

Step 7