Algebra Examples

$3 x + y = 16$ , $2 x - 6 y - 36$

Step 1

Subtract $y$ from both sides of the equation.

$3 x = 16 - y$

Step 2

Divide each term in $3 x = 16 - y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x = 16 - y$ by $3$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

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

Step 3

Replace the variable $x$ with $\frac{16}{3} - \frac{y}{3}$ in the expression.

$2 (\frac{16}{3} - \frac{y}{3}) - 6 y - 36$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$2 (\frac{16}{3}) + 2 (- \frac{y}{3}) - 6 y - 36$

Step 4.2

Multiply $2 (\frac{16}{3})$ .

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Step 4.2.1

Combine $2$ and $\frac{16}{3}$ .

$\frac{2 \cdot 16}{3} + 2 (- \frac{y}{3}) - 6 y - 36$

Step 4.2.2

Multiply $2$ by $16$ .

$\frac{32}{3} + 2 (- \frac{y}{3}) - 6 y - 36$

Step 4.3

Multiply $2 (- \frac{y}{3})$ .

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Step 4.3.1

Multiply $- 1$ by $2$ .

$\frac{32}{3} - 2 \frac{y}{3} - 6 y - 36$

Step 4.3.2

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

$\frac{32}{3} + \frac{- 2 y}{3} - 6 y - 36$

Step 4.4

Move the negative in front of the fraction.

$\frac{32}{3} - \frac{2 y}{3} - 6 y - 36$

Step 5

To write $- 36$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{2 y}{3} - 6 y + \frac{32}{3} - 36 \cdot \frac{3}{3}$

Step 6

Combine $- 36$ and $\frac{3}{3}$ .

$- \frac{2 y}{3} - 6 y + \frac{32}{3} + \frac{- 36 \cdot 3}{3}$

Step 7

Combine the numerators over the common denominator.

$- \frac{2 y}{3} - 6 y + \frac{32 - 36 \cdot 3}{3}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 36$ by $3$ .

$- \frac{2 y}{3} - 6 y + \frac{32 - 108}{3}$

Step 8.2

Subtract $108$ from $32$ .

$- \frac{2 y}{3} - 6 y + \frac{- 76}{3}$

Step 9

Move the negative in front of the fraction.

$- \frac{2 y}{3} - 6 y - \frac{76}{3}$

Step 10

To write $- 6 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{2 y}{3} - 6 y \cdot \frac{3}{3} - \frac{76}{3}$

Step 11

Combine $- 6 y$ and $\frac{3}{3}$ .

$- \frac{2 y}{3} + \frac{- 6 y \cdot 3}{3} - \frac{76}{3}$

Step 12

Combine the numerators over the common denominator.

$\frac{- 2 y - 6 y \cdot 3}{3} - \frac{76}{3}$

Step 13

Combine the numerators over the common denominator.

$\frac{- 2 y - 6 y \cdot 3 - 76}{3}$

Step 14

Multiply $3$ by $- 6$ .

$\frac{- 2 y - 18 y - 76}{3}$

Step 15

Subtract $18 y$ from $- 2 y$ .

$\frac{- 20 y - 76}{3}$

Step 16

Factor $4$ out of $- 20 y - 76$ .

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Step 16.1

Factor $4$ out of $- 20 y$ .

$\frac{4 (- 5 y) - 76}{3}$

Step 16.2

Factor $4$ out of $- 76$ .

$\frac{4 (- 5 y) + 4 (- 19)}{3}$

Step 16.3

Factor $4$ out of $4 (- 5 y) + 4 (- 19)$ .

$\frac{4 (- 5 y - 19)}{3}$

Step 17

Factor $- 1$ out of $- 5 y$ .

$\frac{4 (- (5 y) - 19)}{3}$

Step 18

Rewrite $- 19$ as $- 1 (19)$ .

$\frac{4 (- (5 y) - 1 (19))}{3}$

Step 19

Factor $- 1$ out of $- (5 y) - 1 (19)$ .

$\frac{4 (- (5 y + 19))}{3}$

Step 20

Simplify the expression.

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Step 20.1

Rewrite $- (5 y + 19)$ as $- 1 (5 y + 19)$ .

$\frac{4 (- 1 (5 y + 19))}{3}$

Step 20.2

Move the negative in front of the fraction.

$- \frac{4 (5 y + 19)}{3}$