Determine if Linear 2x+3y=9xy

$2 x + 3 y = 9 x y$

Solve the equation for $y$ .

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

$2 x + 3 y - 9 x y = 0$

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

$3 y - 9 x y = - 2 x$

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

Factor $3 y$ out of $3 y$ .

$3 y (1) - 9 x y = - 2 x$

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

$3 y (1) + 3 y (- 3 x) = - 2 x$

Factor $3 y$ out of $3 y (1) + 3 y (- 3 x)$ .

$3 y (1 - 3 x) = - 2 x$

Divide each term in $3 y (1 - 3 x) = - 2 x$ by $3 (1 - 3 x)$ and simplify.

Divide each term in $3 y (1 - 3 x) = - 2 x$ by $3 (1 - 3 x)$ .

$\frac{3 y (1 - 3 x)}{3 (1 - 3 x)} = \frac{- 2 x}{3 (1 - 3 x)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y (1 - 3 x)}{3 (1 - 3 x)} = \frac{- 2 x}{3 (1 - 3 x)}$

Rewrite the expression.

$\frac{y (1 - 3 x)}{1 - 3 x} = \frac{- 2 x}{3 (1 - 3 x)}$

Cancel the common factor of $1 - 3 x$ .

Cancel the common factor.

$\frac{y (1 - 3 x)}{1 - 3 x} = \frac{- 2 x}{3 (1 - 3 x)}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{3 (1 - 3 x)}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{2 x}{3 (1 - 3 x)}$

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 2x+3y=9xy

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