Algebra Examples

$\frac{11 x + y}{3} + 6 y = 10$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $\frac{11 x + y}{3} + 6 y$ .

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Step 1.1.1

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

$\frac{11 x + y}{3} + 6 y \cdot \frac{3}{3} = 10$

Step 1.1.2

Simplify terms.

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Step 1.1.2.1

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

$\frac{11 x + y}{3} + \frac{6 y \cdot 3}{3} = 10$

Step 1.1.2.2

Combine the numerators over the common denominator.

$\frac{11 x + y + 6 y \cdot 3}{3} = 10$

Step 1.1.3

Simplify the numerator.

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Step 1.1.3.1

Multiply $3$ by $6$ .

$\frac{11 x + y + 18 y}{3} = 10$

Step 1.1.3.2

Add $y$ and $18 y$ .

$\frac{11 x + 19 y}{3} = 10$

Step 1.2

Multiply both sides by $3$ .

$\frac{11 x + 19 y}{3} \cdot 3 = 10 \cdot 3$

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 $3$ .

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Step 1.3.1.1.1

Cancel the common factor.

$\frac{11 x + 19 y}{3} \cdot 3 = 10 \cdot 3$

Step 1.3.1.1.2

Rewrite the expression.

$11 x + 19 y = 10 \cdot 3$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Multiply $10$ by $3$ .

$11 x + 19 y = 30$

Step 1.4

Solve for $y$ .

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Step 1.4.1

Subtract $11 x$ from both sides of the equation.

$19 y = 30 - 11 x$

Step 1.4.2

Divide each term in $19 y = 30 - 11 x$ by $19$ and simplify.

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Step 1.4.2.1

Divide each term in $19 y = 30 - 11 x$ by $19$ .

$\frac{19 y}{19} = \frac{30}{19} + \frac{- 11 x}{19}$

Step 1.4.2.2

Simplify the left side.

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Step 1.4.2.2.1

Cancel the common factor of $19$ .

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Step 1.4.2.2.1.1

Cancel the common factor.

$\frac{19 y}{19} = \frac{30}{19} + \frac{- 11 x}{19}$

Step 1.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{30}{19} + \frac{- 11 x}{19}$

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.

$y = \frac{30}{19} - \frac{11 x}{19}$

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