Determine if Linear 5x+4xy=2y

$5 x + 4 x y = 2 y$

Step 1

Solve the equation for $y$ .

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

$5 x + 4 x y - 2 y = 0$

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

$4 x y - 2 y = - 5 x$

Factor $2 y$ out of $4 x y - 2 y$ .

Factor $2 y$ out of $4 x y$ .

$2 y (2 x) - 2 y = - 5 x$

Factor $2 y$ out of $- 2 y$ .

$2 y (2 x) + 2 y (- 1) = - 5 x$

Factor $2 y$ out of $2 y (2 x) + 2 y (- 1)$ .

$2 y (2 x - 1) = - 5 x$

Divide each term in $2 y (2 x - 1) = - 5 x$ by $2 (2 x - 1)$ and simplify.

Divide each term in $2 y (2 x - 1) = - 5 x$ by $2 (2 x - 1)$ .

$\frac{2 y (2 x - 1)}{2 (2 x - 1)} = \frac{- 5 x}{2 (2 x - 1)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y (2 x - 1)}{2 (2 x - 1)} = \frac{- 5 x}{2 (2 x - 1)}$

Rewrite the expression.

$\frac{y (2 x - 1)}{2 x - 1} = \frac{- 5 x}{2 (2 x - 1)}$

Cancel the common factor of $2 x - 1$ .

Cancel the common factor.

$\frac{y (2 x - 1)}{2 x - 1} = \frac{- 5 x}{2 (2 x - 1)}$

Divide $y$ by $1$ .

$y = \frac{- 5 x}{2 (2 x - 1)}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{5 x}{2 (2 x - 1)}$

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 $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear

Determine if Linear 5x+4xy=2y

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