Determine if Linear (2x-y)/5+12y=10

$\frac{2 x - y}{5} + 12 y = 10$

Step 1

Solve the equation for $y$ .

Simplify $\frac{2 x - y}{5} + 12 y$ .

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

$\frac{2 x - y}{5} + 12 y \cdot \frac{5}{5} = 10$

Simplify terms.

Combine $12 y$ and $\frac{5}{5}$ .

$\frac{2 x - y}{5} + \frac{12 y \cdot 5}{5} = 10$

Combine the numerators over the common denominator.

$\frac{2 x - y + 12 y \cdot 5}{5} = 10$

Simplify the numerator.

Multiply $5$ by $12$ .

$\frac{2 x - y + 60 y}{5} = 10$

Add $- y$ and $60 y$ .

$\frac{2 x + 59 y}{5} = 10$

Multiply both sides by $5$ .

$\frac{2 x + 59 y}{5} \cdot 5 = 10 \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 x + 59 y}{5} \cdot 5 = 10 \cdot 5$

Rewrite the expression.

$2 x + 59 y = 10 \cdot 5$

Simplify the right side.

Multiply $10$ by $5$ .

$2 x + 59 y = 50$

Solve for $y$ .

Subtract $2 x$ from both sides of the equation.

$59 y = 50 - 2 x$

Divide each term in $59 y = 50 - 2 x$ by $59$ and simplify.

Divide each term in $59 y = 50 - 2 x$ by $59$ .

$\frac{59 y}{59} = \frac{50}{59} + \frac{- 2 x}{59}$

Simplify the left side.

Cancel the common factor of $59$ .

Cancel the common factor.

$\frac{59 y}{59} = \frac{50}{59} + \frac{- 2 x}{59}$

Divide $y$ by $1$ .

$y = \frac{50}{59} + \frac{- 2 x}{59}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{50}{59} - \frac{2 x}{59}$

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

Determine if Linear (2x-y)/5+12y=10

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