Determine if Linear (11x+y)/4+2y=7

$\frac{11 x + y}{4} + 2 y = 7$

Step 1

Solve the equation for $y$ .

Simplify $\frac{11 x + y}{4} + 2 y$ .

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{11 x + y}{4} + 2 y \cdot \frac{4}{4} = 7$

Simplify terms.

Combine $2 y$ and $\frac{4}{4}$ .

$\frac{11 x + y}{4} + \frac{2 y \cdot 4}{4} = 7$

Combine the numerators over the common denominator.

$\frac{11 x + y + 2 y \cdot 4}{4} = 7$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{11 x + y + 8 y}{4} = 7$

Add $y$ and $8 y$ .

$\frac{11 x + 9 y}{4} = 7$

Multiply both sides by $4$ .

$\frac{11 x + 9 y}{4} \cdot 4 = 7 \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{11 x + 9 y}{4} \cdot 4 = 7 \cdot 4$

Rewrite the expression.

$11 x + 9 y = 7 \cdot 4$

Simplify the right side.

Multiply $7$ by $4$ .

$11 x + 9 y = 28$

Solve for $y$ .

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

$9 y = 28 - 11 x$

Divide each term in $9 y = 28 - 11 x$ by $9$ and simplify.

Divide each term in $9 y = 28 - 11 x$ by $9$ .

$\frac{9 y}{9} = \frac{28}{9} + \frac{- 11 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{28}{9} + \frac{- 11 x}{9}$

Divide $y$ by $1$ .

$y = \frac{28}{9} + \frac{- 11 x}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{28}{9} - \frac{11 x}{9}$

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 (11x+y)/4+2y=7

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