Algebra Examples

$8 x - 25 - 9 y$ , $- 13 x = - 35 + 9 y$

Step 1

Divide each term in $- 13 x = - 35 + 9 y$ by $- 13$ and simplify.

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Step 1.1

Divide each term in $- 13 x = - 35 + 9 y$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 35}{- 13} + \frac{9 y}{- 13}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 13$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 35}{- 13} + \frac{9 y}{- 13}$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 35}{- 13} + \frac{9 y}{- 13}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{35}{13} + \frac{9 y}{- 13}$

Step 1.3.1.2

Move the negative in front of the fraction.

$x = \frac{35}{13} - \frac{9 y}{13}$

Step 2

Replace the variable $x$ with $\frac{35}{13} - \frac{9 y}{13}$ in the expression.

$8 (\frac{35}{13} - \frac{9 y}{13}) - 25 - 9 y$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$8 (\frac{35}{13}) + 8 (- \frac{9 y}{13}) - 25 - 9 y$

Step 3.2

Multiply $8 (\frac{35}{13})$ .

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Step 3.2.1

Combine $8$ and $\frac{35}{13}$ .

$\frac{8 \cdot 35}{13} + 8 (- \frac{9 y}{13}) - 25 - 9 y$

Step 3.2.2

Multiply $8$ by $35$ .

$\frac{280}{13} + 8 (- \frac{9 y}{13}) - 25 - 9 y$

Step 3.3

Multiply $8 (- \frac{9 y}{13})$ .

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Step 3.3.1

Multiply $- 1$ by $8$ .

$\frac{280}{13} - 8 \frac{9 y}{13} - 25 - 9 y$

Step 3.3.2

Combine $- 8$ and $\frac{9 y}{13}$ .

$\frac{280}{13} + \frac{- 8 (9 y)}{13} - 25 - 9 y$

Step 3.3.3

Multiply $9$ by $- 8$ .

$\frac{280}{13} + \frac{- 72 y}{13} - 25 - 9 y$

Step 3.4

Move the negative in front of the fraction.

$\frac{280}{13} - \frac{72 y}{13} - 25 - 9 y$

Step 4

To write $- 25$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$- \frac{72 y}{13} + \frac{280}{13} - 25 \cdot \frac{13}{13} - 9 y$

Step 5

Combine $- 25$ and $\frac{13}{13}$ .

$- \frac{72 y}{13} + \frac{280}{13} + \frac{- 25 \cdot 13}{13} - 9 y$

Step 6

Combine the numerators over the common denominator.

$- \frac{72 y}{13} + \frac{280 - 25 \cdot 13}{13} - 9 y$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 25$ by $13$ .

$- \frac{72 y}{13} + \frac{280 - 325}{13} - 9 y$

Step 7.2

Subtract $325$ from $280$ .

$- \frac{72 y}{13} + \frac{- 45}{13} - 9 y$

Step 8

Move the negative in front of the fraction.

$- \frac{72 y}{13} - \frac{45}{13} - 9 y$

Step 9

To write $- 9 y$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$- \frac{72 y}{13} - 9 y \cdot \frac{13}{13} - \frac{45}{13}$

Step 10

Combine $- 9 y$ and $\frac{13}{13}$ .

$- \frac{72 y}{13} + \frac{- 9 y \cdot 13}{13} - \frac{45}{13}$

Step 11

Combine the numerators over the common denominator.

$\frac{- 72 y - 9 y \cdot 13}{13} - \frac{45}{13}$

Step 12

Combine the numerators over the common denominator.

$\frac{- 72 y - 9 y \cdot 13 - 45}{13}$

Step 13

Multiply $13$ by $- 9$ .

$\frac{- 72 y - 117 y - 45}{13}$

Step 14

Subtract $117 y$ from $- 72 y$ .

$\frac{- 189 y - 45}{13}$

Step 15

Factor $9$ out of $- 189 y - 45$ .

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Step 15.1

Factor $9$ out of $- 189 y$ .

$\frac{9 (- 21 y) - 45}{13}$

Step 15.2

Factor $9$ out of $- 45$ .

$\frac{9 (- 21 y) + 9 (- 5)}{13}$

Step 15.3

Factor $9$ out of $9 (- 21 y) + 9 (- 5)$ .

$\frac{9 (- 21 y - 5)}{13}$

Step 16

Factor $- 1$ out of $- 21 y$ .

$\frac{9 (- (21 y) - 5)}{13}$

Step 17

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{9 (- (21 y) - 1 (5))}{13}$

Step 18

Factor $- 1$ out of $- (21 y) - 1 (5)$ .

$\frac{9 (- (21 y + 5))}{13}$

Step 19

Simplify the expression.

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Step 19.1

Rewrite $- (21 y + 5)$ as $- 1 (21 y + 5)$ .

$\frac{9 (- 1 (21 y + 5))}{13}$

Step 19.2

Move the negative in front of the fraction.

$- \frac{9 (21 y + 5)}{13}$