Determine if Linear 8x+5xy=9y

$8 x + 5 x y = 9 y$

Step 1

Solve the equation for $y$ .

Subtract $9 y$ from both sides of the equation.

$8 x + 5 x y - 9 y = 0$

Subtract $8 x$ from both sides of the equation.

$5 x y - 9 y = - 8 x$

Factor $y$ out of $5 x y - 9 y$ .

Factor $y$ out of $5 x y$ .

$y (5 x) - 9 y = - 8 x$

Factor $y$ out of $- 9 y$ .

$y (5 x) + y \cdot - 9 = - 8 x$

Factor $y$ out of $y (5 x) + y \cdot - 9$ .

$y (5 x - 9) = - 8 x$

Divide each term in $y (5 x - 9) = - 8 x$ by $5 x - 9$ and simplify.

Divide each term in $y (5 x - 9) = - 8 x$ by $5 x - 9$ .

$\frac{y (5 x - 9)}{5 x - 9} = \frac{- 8 x}{5 x - 9}$

Simplify the left side.

Cancel the common factor of $5 x - 9$ .

Cancel the common factor.

$\frac{y (5 x - 9)}{5 x - 9} = \frac{- 8 x}{5 x - 9}$

Divide $y$ by $1$ .

$y = \frac{- 8 x}{5 x - 9}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{8 x}{5 x - 9}$

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 $1$ , 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 8x+5xy=9y

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