Algebra Examples

$- \frac{10 x}{3} - \frac{5 y}{8} = \frac{145}{12}$ $- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1

Solve for $x$ in $- \frac{10 x}{3} - \frac{5 y}{8} = \frac{145}{12}$ .

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Step 1.1

Add $\frac{5 y}{8}$ to both sides of the equation.

$- \frac{10 x}{3} = \frac{145}{12} + \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.2

Multiply both sides of the equation by $- \frac{3}{10}$ .

$- \frac{3}{10} \cdot (- \frac{10 x}{3}) = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Simplify $- \frac{3}{10} (- \frac{10 x}{3})$ .

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Step 1.3.1.1.1

Cancel the common factor of $3$ .

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Step 1.3.1.1.1.1

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$\frac{- 3}{10} \cdot (- \frac{10 x}{3}) = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.1.2

Move the leading negative in $- \frac{10 x}{3}$ into the numerator.

$\frac{- 3}{10} \cdot \frac{- 10 x}{3} = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{10} \cdot \frac{- 10 x}{3} = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{10} \cdot \frac{- 10 x}{3} = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{10} \cdot (- 10 x) = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$\frac{- 1}{10} \cdot (- 10 x) = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.2

Cancel the common factor of $10$ .

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Step 1.3.1.1.2.1

Factor $10$ out of $- 10 x$ .

$\frac{- 1}{10} \cdot (10 (- x)) = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{10} \cdot (10 (- x)) = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.2.3

Rewrite the expression.

$x = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.3

Multiply.

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Step 1.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3}{10} \cdot (\frac{145}{12} + \frac{5 y}{8})$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $- \frac{3}{10} (\frac{145}{12} + \frac{5 y}{8})$ .

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Step 1.3.2.1.1

Simplify terms.

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Step 1.3.2.1.1.1

Apply the distributive property.

$x = - \frac{3}{10} \cdot \frac{145}{12} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.2

Cancel the common factor of $3$ .

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Step 1.3.2.1.1.2.1

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$x = \frac{- 3}{10} \cdot \frac{145}{12} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.2.2

Factor $3$ out of $- 3$ .

$x = \frac{3 (- 1)}{10} \cdot \frac{145}{12} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.2.3

Factor $3$ out of $12$ .

$x = \frac{3 \cdot - 1}{10} \cdot \frac{145}{3 \cdot 4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.2.4

Cancel the common factor.

$x = \frac{3 \cdot - 1}{10} \cdot \frac{145}{3 \cdot 4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.2.5

Rewrite the expression.

$x = \frac{- 1}{10} \cdot \frac{145}{4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = \frac{- 1}{10} \cdot \frac{145}{4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.3

Cancel the common factor of $5$ .

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Step 1.3.2.1.1.3.1

Factor $5$ out of $10$ .

$x = \frac{- 1}{5 (2)} \cdot \frac{145}{4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.3.2

Factor $5$ out of $145$ .

$x = \frac{- 1}{5 \cdot 2} \cdot \frac{5 \cdot 29}{4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.3.3

Cancel the common factor.

$x = \frac{- 1}{5 \cdot 2} \cdot \frac{5 \cdot 29}{4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.3.4

Rewrite the expression.

$x = \frac{- 1}{2} \cdot \frac{29}{4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = \frac{- 1}{2} \cdot \frac{29}{4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.4

Multiply $\frac{- 1}{2}$ by $\frac{29}{4}$ .

$x = \frac{- 1 \cdot 29}{2 \cdot 4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.5

Multiply.

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Step 1.3.2.1.1.5.1

Multiply $- 1$ by $29$ .

$x = \frac{- 29}{2 \cdot 4} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.5.2

Multiply $2$ by $4$ .

$x = \frac{- 29}{8} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = \frac{- 29}{8} - \frac{3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.6

Cancel the common factor of $5$ .

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Step 1.3.2.1.1.6.1

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$x = \frac{- 29}{8} + \frac{- 3}{10} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.6.2

Factor $5$ out of $10$ .

$x = \frac{- 29}{8} + \frac{- 3}{5 (2)} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.6.3

Factor $5$ out of $5 y$ .

$x = \frac{- 29}{8} + \frac{- 3}{5 (2)} \cdot \frac{5 (y)}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.6.4

Cancel the common factor.

$x = \frac{- 29}{8} + \frac{- 3}{5 \cdot 2} \cdot \frac{5 y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.6.5

Rewrite the expression.

$x = \frac{- 29}{8} + \frac{- 3}{2} \cdot \frac{y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = \frac{- 29}{8} + \frac{- 3}{2} \cdot \frac{y}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.7

Multiply $\frac{- 3}{2}$ by $\frac{y}{8}$ .

$x = \frac{- 29}{8} + \frac{- 3 y}{2 \cdot 8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.1.8

Multiply $2$ by $8$ .

$x = \frac{- 29}{8} + \frac{- 3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = \frac{- 29}{8} + \frac{- 3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.2

Simplify each term.

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Step 1.3.2.1.2.1

Move the negative in front of the fraction.

$x = - \frac{29}{8} + \frac{- 3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.3.2.1.2.2

Move the negative in front of the fraction.

$x = - \frac{29}{8} - \frac{3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{29}{8} - \frac{3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{29}{8} - \frac{3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{29}{8} - \frac{3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{29}{8} - \frac{3 y}{16}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 1.4

Reorder $- \frac{29}{8}$ and $- \frac{3 y}{16}$ .

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$

Step 2

Replace all occurrences of $x$ with $- \frac{3 y}{16} - \frac{29}{8}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- \frac{2 x}{5} - \frac{3 y}{8} = \frac{17}{20}$ with $- \frac{3 y}{16} - \frac{29}{8}$ .

$- \frac{2 (- \frac{3 y}{16} - \frac{29}{8})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- \frac{2 (- \frac{3 y}{16} - \frac{29}{8})}{5} - \frac{3 y}{8}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Simplify the numerator.

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Step 2.2.1.1.1.1

Factor $- 1$ out of $- \frac{3 y}{16} - \frac{29}{8}$ .

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Step 2.2.1.1.1.1.1

Factor $- 1$ out of $- \frac{3 y}{16}$ .

$- \frac{2 (- (\frac{3 y}{16}) - \frac{29}{8})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.1.2

Factor $- 1$ out of $- \frac{29}{8}$ .

$- \frac{2 (- (\frac{3 y}{16}) - (\frac{29}{8}))}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.1.3

Factor $- 1$ out of $- (\frac{3 y}{16}) - (\frac{29}{8})$ .

$- \frac{2 (- (\frac{3 y}{16} + \frac{29}{8}))}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{2 \cdot (- 1 (\frac{3 y}{16} + \frac{29}{8}))}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.2

Combine exponents.

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Step 2.2.1.1.1.2.1

Factor out negative.

$- \frac{- (2 (\frac{3 y}{16} + \frac{29}{8}))}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.2.2

Multiply $2$ by $- 1$ .

$- \frac{- 2 (\frac{3 y}{16} + \frac{29}{8})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{- 2 (\frac{3 y}{16} + \frac{29}{8})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.3

To write $\frac{29}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{- 2 (\frac{3 y}{16} + \frac{29}{8} \cdot \frac{2}{2})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.4

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.1.1.4.1

Multiply $\frac{29}{8}$ by $\frac{2}{2}$ .

$- \frac{- 2 (\frac{3 y}{16} + \frac{29 \cdot 2}{8 \cdot 2})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.4.2

Multiply $8$ by $2$ .

$- \frac{- 2 (\frac{3 y}{16} + \frac{29 \cdot 2}{16})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{- 2 (\frac{3 y}{16} + \frac{29 \cdot 2}{16})}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.5

Combine the numerators over the common denominator.

$- \frac{- 2 \frac{3 y + 29 \cdot 2}{16}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.1.6

Multiply $29$ by $2$ .

$- \frac{- 2 \frac{3 y + 58}{16}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{- 2 \frac{3 y + 58}{16}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.2

Combine $- 2$ and $\frac{3 y + 58}{16}$ .

$- \frac{\frac{- 2 (3 y + 58)}{16}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.3

Simplify the numerator.

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Step 2.2.1.1.3.1

Reduce the expression $\frac{- 2 (3 y + 58)}{16}$ by cancelling the common factors.

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Step 2.2.1.1.3.1.1

Factor $2$ out of $- 2 (3 y + 58)$ .

$- \frac{\frac{2 (- (3 y + 58))}{16}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.3.1.2

Factor $2$ out of $16$ .

$- \frac{\frac{2 (- (3 y + 58))}{2 (8)}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.3.1.3

Cancel the common factor.

$- \frac{\frac{2 (- (3 y + 58))}{2 \cdot 8}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.3.1.4

Rewrite the expression.

$- \frac{\frac{- (3 y + 58)}{8}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{\frac{- (3 y + 58)}{8}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.3.2

Move the negative in front of the fraction.

$- \frac{- \frac{3 y + 58}{8}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{- \frac{3 y + 58}{8}}{5} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.4

Multiply the numerator by the reciprocal of the denominator.

$- (- \frac{3 y + 58}{8} \cdot \frac{1}{5}) - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.5

Multiply $- \frac{3 y + 58}{8} \cdot \frac{1}{5}$ .

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Step 2.2.1.1.5.1

Multiply $\frac{1}{5}$ by $\frac{3 y + 58}{8}$ .

$\frac{3 y + 58}{5 \cdot 8} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.5.2

Multiply $5$ by $8$ .

$\frac{3 y + 58}{40} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$\frac{3 y + 58}{40} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.6

Multiply $- - \frac{3 y + 58}{40}$ .

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Step 2.2.1.1.6.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{3 y + 58}{40}) - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.1.6.2

Multiply $\frac{3 y + 58}{40}$ by $1$ .

$\frac{3 y + 58}{40} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$\frac{3 y + 58}{40} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$\frac{3 y + 58}{40} - \frac{3 y}{8} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.2

To write $- \frac{3 y}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 y + 58}{40} - \frac{3 y}{8} \cdot \frac{5}{5} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.3.1

Multiply $\frac{3 y}{8}$ by $\frac{5}{5}$ .

$\frac{3 y + 58}{40} - \frac{3 y \cdot 5}{8 \cdot 5} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.3.2

Multiply $8$ by $5$ .

$\frac{3 y + 58}{40} - \frac{3 y \cdot 5}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$\frac{3 y + 58}{40} - \frac{3 y \cdot 5}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{3 y + 58 - 3 y \cdot 5}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.5

Simplify the numerator.

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Step 2.2.1.5.1

Multiply $5$ by $- 3$ .

$\frac{3 y + 58 - 15 y}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.5.2

Subtract $15 y$ from $3 y$ .

$\frac{- 12 y + 58}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.5.3

Factor $2$ out of $- 12 y + 58$ .

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Step 2.2.1.5.3.1

Factor $2$ out of $- 12 y$ .

$\frac{2 (- 6 y) + 58}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.5.3.2

Factor $2$ out of $58$ .

$\frac{2 (- 6 y) + 2 (29)}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.5.3.3

Factor $2$ out of $2 (- 6 y) + 2 (29)$ .

$\frac{2 (- 6 y + 29)}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$\frac{2 (- 6 y + 29)}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$\frac{2 (- 6 y + 29)}{40} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.6

Cancel the common factors.

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Step 2.2.1.6.1

Factor $2$ out of $40$ .

$\frac{2 (- 6 y + 29)}{2 \cdot 20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.6.2

Cancel the common factor.

$\frac{2 (- 6 y + 29)}{2 \cdot 20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.6.3

Rewrite the expression.

$\frac{- 6 y + 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$\frac{- 6 y + 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.7

Factor $- 1$ out of $- 6 y$ .

$\frac{- (6 y) + 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.8

Rewrite $29$ as $- 1 (- 29)$ .

$\frac{- (6 y) - 1 \cdot - 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.9

Factor $- 1$ out of $- (6 y) - 1 (- 29)$ .

$\frac{- (6 y - 29)}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.10

Simplify the expression.

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Step 2.2.1.10.1

Rewrite $- (6 y - 29)$ as $- 1 (6 y - 29)$ .

$\frac{- 1 (6 y - 29)}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 2.2.1.10.2

Move the negative in front of the fraction.

$- \frac{6 y - 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{6 y - 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{6 y - 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{6 y - 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- \frac{6 y - 29}{20} = \frac{17}{20}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3

Solve for $y$ in $- \frac{6 y - 29}{20} = \frac{17}{20}$ .

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Step 3.1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- (6 y - 29) = 17$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.2

Simplify $- (6 y - 29)$ .

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Step 3.2.1

Apply the distributive property.

$- (6 y) + 29 = 17$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.2.2

Multiply.

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Step 3.2.2.1

Multiply $6$ by $- 1$ .

$- 6 y + 29 = 17$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.2.2.2

Multiply $- 1$ by $- 29$ .

$- 6 y + 29 = 17$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- 6 y + 29 = 17$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- 6 y + 29 = 17$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.3

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

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Step 3.3.1

Subtract $29$ from both sides of the equation.

$- 6 y = 17 - 29$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.3.2

Subtract $29$ from $17$ .

$- 6 y = - 12$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$- 6 y = - 12$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.4

Divide each term in $- 6 y = - 12$ by $- 6$ and simplify.

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Step 3.4.1

Divide each term in $- 6 y = - 12$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 12}{- 6}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $- 6$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 12}{- 6}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{- 6}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$y = \frac{- 12}{- 6}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$y = \frac{- 12}{- 6}$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $- 12$ by $- 6$ .

$y = 2$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$y = 2$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$y = 2$

$x = - \frac{3 y}{16} - \frac{29}{8}$

$y = 2$

$x = - \frac{3 y}{16} - \frac{29}{8}$

Step 4

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

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Step 4.1

Replace all occurrences of $y$ in $x = - \frac{3 y}{16} - \frac{29}{8}$ with $2$ .

$x = - \frac{3 (2)}{16} - \frac{29}{8}$

$y = 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{3 (2)}{16} - \frac{29}{8}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ and $16$ .

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Step 4.2.1.1.1

Factor $2$ out of $3 (2)$ .

$x = - \frac{2 \cdot 3}{16} - \frac{29}{8}$

$y = 2$

Step 4.2.1.1.2

Cancel the common factors.

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Step 4.2.1.1.2.1

Factor $2$ out of $16$ .

$x = - \frac{2 \cdot 3}{2 \cdot 8} - \frac{29}{8}$

$y = 2$

Step 4.2.1.1.2.2

Cancel the common factor.

$x = - \frac{2 \cdot 3}{2 \cdot 8} - \frac{29}{8}$

$y = 2$

Step 4.2.1.1.2.3

Rewrite the expression.

$x = - \frac{3}{8} - \frac{29}{8}$

$y = 2$

$x = - \frac{3}{8} - \frac{29}{8}$

$y = 2$

$x = - \frac{3}{8} - \frac{29}{8}$

$y = 2$

Step 4.2.1.2

Combine the numerators over the common denominator.

$x = \frac{- 3 - 29}{8}$

$y = 2$

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Subtract $29$ from $- 3$ .

$x = \frac{- 32}{8}$

$y = 2$

Step 4.2.1.3.2

Divide $- 32$ by $8$ .

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

Step 5

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

$(- 4, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, 2)$

Equation Form:

$x = - 4, y = 2$

Step 7