Determine if Linear (4x-y)/3+7y=8

$\frac{4 x - y}{3} + 7 y = 8$

Step 1

Solve the equation for $y$ .

Simplify $\frac{4 x - y}{3} + 7 y$ .

To write $7 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 x - y}{3} + 7 y \cdot \frac{3}{3} = 8$

Simplify terms.

Combine $7 y$ and $\frac{3}{3}$ .

$\frac{4 x - y}{3} + \frac{7 y \cdot 3}{3} = 8$

Combine the numerators over the common denominator.

$\frac{4 x - y + 7 y \cdot 3}{3} = 8$

Simplify the numerator.

Multiply $3$ by $7$ .

$\frac{4 x - y + 21 y}{3} = 8$

Add $- y$ and $21 y$ .

$\frac{4 x + 20 y}{3} = 8$

Factor $4$ out of $4 x + 20 y$ .

Factor $4$ out of $4 x$ .

$\frac{4 (x) + 20 y}{3} = 8$

Factor $4$ out of $20 y$ .

$\frac{4 (x) + 4 (5 y)}{3} = 8$

Factor $4$ out of $4 (x) + 4 (5 y)$ .

$\frac{4 (x + 5 y)}{3} = 8$

Multiply both sides by $3$ .

$\frac{4 (x + 5 y)}{3} \cdot 3 = 8 \cdot 3$

Simplify.

Simplify the left side.

Simplify $\frac{4 (x + 5 y)}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4 (x + 5 y)}{3} \cdot 3 = 8 \cdot 3$

Rewrite the expression.

$4 (x + 5 y) = 8 \cdot 3$

Apply the distributive property.

$4 x + 4 (5 y) = 8 \cdot 3$

Multiply $5$ by $4$ .

$4 x + 20 y = 8 \cdot 3$

Simplify the right side.

Multiply $8$ by $3$ .

$4 x + 20 y = 24$

Solve for $y$ .

Subtract $4 x$ from both sides of the equation.

$20 y = 24 - 4 x$

Divide each term in $20 y = 24 - 4 x$ by $20$ and simplify.

Divide each term in $20 y = 24 - 4 x$ by $20$ .

$\frac{20 y}{20} = \frac{24}{20} + \frac{- 4 x}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 y}{20} = \frac{24}{20} + \frac{- 4 x}{20}$

Divide $y$ by $1$ .

$y = \frac{24}{20} + \frac{- 4 x}{20}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $24$ and $20$ .

Factor $4$ out of $24$ .

$y = \frac{4 (6)}{20} + \frac{- 4 x}{20}$

Cancel the common factors.

Factor $4$ out of $20$ .

$y = \frac{4 \cdot 6}{4 \cdot 5} + \frac{- 4 x}{20}$

Cancel the common factor.

$y = \frac{4 \cdot 6}{4 \cdot 5} + \frac{- 4 x}{20}$

Rewrite the expression.

$y = \frac{6}{5} + \frac{- 4 x}{20}$

Cancel the common factor of $- 4$ and $20$ .

Factor $4$ out of $- 4 x$ .

$y = \frac{6}{5} + \frac{4 (- x)}{20}$

Cancel the common factors.

Factor $4$ out of $20$ .

$y = \frac{6}{5} + \frac{4 (- x)}{4 (5)}$

Cancel the common factor.

$y = \frac{6}{5} + \frac{4 (- x)}{4 \cdot 5}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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 (4x-y)/3+7y=8

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