Determine if Linear 4x+6xy=9y

$4 x + 6 x y = 9 y$

Step 1

Solve the equation for $y$ .

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

$4 x + 6 x y - 9 y = 0$

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

$6 x y - 9 y = - 4 x$

Factor $3 y$ out of $6 x y - 9 y$ .

Factor $3 y$ out of $6 x y$ .

$3 y (2 x) - 9 y = - 4 x$

Factor $3 y$ out of $- 9 y$ .

$3 y (2 x) + 3 y (- 3) = - 4 x$

Factor $3 y$ out of $3 y (2 x) + 3 y (- 3)$ .

$3 y (2 x - 3) = - 4 x$

Divide each term in $3 y (2 x - 3) = - 4 x$ by $3 (2 x - 3)$ and simplify.

Divide each term in $3 y (2 x - 3) = - 4 x$ by $3 (2 x - 3)$ .

$\frac{3 y (2 x - 3)}{3 (2 x - 3)} = \frac{- 4 x}{3 (2 x - 3)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y (2 x - 3)}{3 (2 x - 3)} = \frac{- 4 x}{3 (2 x - 3)}$

Rewrite the expression.

$\frac{y (2 x - 3)}{2 x - 3} = \frac{- 4 x}{3 (2 x - 3)}$

Cancel the common factor of $2 x - 3$ .

Cancel the common factor.

$\frac{y (2 x - 3)}{2 x - 3} = \frac{- 4 x}{3 (2 x - 3)}$

Divide $y$ by $1$ .

$y = \frac{- 4 x}{3 (2 x - 3)}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{4 x}{3 (2 x - 3)}$

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 4x+6xy=9y

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