Algebra Examples

$\frac{7 x - y}{6} + \frac{12 y}{5} = 11$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $\frac{7 x - y}{6} + \frac{12 y}{5}$ .

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Step 1.1.1

To write $\frac{7 x - y}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7 x - y}{6} \cdot \frac{5}{5} + \frac{12 y}{5} = 11$

Step 1.1.2

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

$\frac{7 x - y}{6} \cdot \frac{5}{5} + \frac{12 y}{5} \cdot \frac{6}{6} = 11$

Step 1.1.3

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

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Step 1.1.3.1

Multiply $\frac{7 x - y}{6}$ by $\frac{5}{5}$ .

$\frac{(7 x - y) \cdot 5}{6 \cdot 5} + \frac{12 y}{5} \cdot \frac{6}{6} = 11$

Step 1.1.3.2

Multiply $6$ by $5$ .

$\frac{(7 x - y) \cdot 5}{30} + \frac{12 y}{5} \cdot \frac{6}{6} = 11$

Step 1.1.3.3

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

$\frac{(7 x - y) \cdot 5}{30} + \frac{12 y \cdot 6}{5 \cdot 6} = 11$

Step 1.1.3.4

Multiply $5$ by $6$ .

$\frac{(7 x - y) \cdot 5}{30} + \frac{12 y \cdot 6}{30} = 11$

Step 1.1.4

Combine the numerators over the common denominator.

$\frac{(7 x - y) \cdot 5 + 12 y \cdot 6}{30} = 11$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Apply the distributive property.

$\frac{7 x \cdot 5 - y \cdot 5 + 12 y \cdot 6}{30} = 11$

Step 1.1.5.2

Multiply $5$ by $7$ .

$\frac{35 x - y \cdot 5 + 12 y \cdot 6}{30} = 11$

Step 1.1.5.3

Multiply $5$ by $- 1$ .

$\frac{35 x - 5 y + 12 y \cdot 6}{30} = 11$

Step 1.1.5.4

Multiply $6$ by $12$ .

$\frac{35 x - 5 y + 72 y}{30} = 11$

Step 1.1.5.5

Add $- 5 y$ and $72 y$ .

$\frac{35 x + 67 y}{30} = 11$

Step 1.2

Multiply both sides by $30$ .

$\frac{35 x + 67 y}{30} \cdot 30 = 11 \cdot 30$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $30$ .

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Step 1.3.1.1.1

Cancel the common factor.

$\frac{35 x + 67 y}{30} \cdot 30 = 11 \cdot 30$

Step 1.3.1.1.2

Rewrite the expression.

$35 x + 67 y = 11 \cdot 30$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Multiply $11$ by $30$ .

$35 x + 67 y = 330$

Step 1.4

Solve for $y$ .

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Step 1.4.1

Subtract $35 x$ from both sides of the equation.

$67 y = 330 - 35 x$

Step 1.4.2

Divide each term in $67 y = 330 - 35 x$ by $67$ and simplify.

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Step 1.4.2.1

Divide each term in $67 y = 330 - 35 x$ by $67$ .

$\frac{67 y}{67} = \frac{330}{67} + \frac{- 35 x}{67}$

Step 1.4.2.2

Simplify the left side.

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Step 1.4.2.2.1

Cancel the common factor of $67$ .

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Step 1.4.2.2.1.1

Cancel the common factor.

$\frac{67 y}{67} = \frac{330}{67} + \frac{- 35 x}{67}$

Step 1.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{330}{67} + \frac{- 35 x}{67}$

Step 1.4.2.3

Simplify the right side.

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Step 1.4.2.3.1

Move the negative in front of the fraction.

$y = \frac{330}{67} - \frac{35 x}{67}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear