Determine if Linear (5x-y)/2+6y=3

$\frac{5 x - y}{2} + 6 y = 3$

Step 1

Solve the equation for $y$ .

Simplify $\frac{5 x - y}{2} + 6 y$ .

To write $6 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x - y}{2} + 6 y \cdot \frac{2}{2} = 3$

Simplify terms.

Combine $6 y$ and $\frac{2}{2}$ .

$\frac{5 x - y}{2} + \frac{6 y \cdot 2}{2} = 3$

Combine the numerators over the common denominator.

$\frac{5 x - y + 6 y \cdot 2}{2} = 3$

Simplify the numerator.

Multiply $2$ by $6$ .

$\frac{5 x - y + 12 y}{2} = 3$

Add $- y$ and $12 y$ .

$\frac{5 x + 11 y}{2} = 3$

Multiply both sides by $2$ .

$\frac{5 x + 11 y}{2} \cdot 2 = 3 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 x + 11 y}{2} \cdot 2 = 3 \cdot 2$

Rewrite the expression.

$5 x + 11 y = 3 \cdot 2$

Simplify the right side.

Multiply $3$ by $2$ .

$5 x + 11 y = 6$

Solve for $y$ .

Subtract $5 x$ from both sides of the equation.

$11 y = 6 - 5 x$

Divide each term in $11 y = 6 - 5 x$ by $11$ and simplify.

Divide each term in $11 y = 6 - 5 x$ by $11$ .

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

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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 (5x-y)/2+6y=3

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