Determine if Linear 9x+10xy=3y

$9 x + 10 x y = 3 y$

Step 1

Solve the equation for $y$ .

Subtract $3 y$ from both sides of the equation.

$9 x + 10 x y - 3 y = 0$

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

$10 x y - 3 y = - 9 x$

Factor $y$ out of $10 x y - 3 y$ .

Factor $y$ out of $10 x y$ .

$y (10 x) - 3 y = - 9 x$

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

$y (10 x) + y \cdot - 3 = - 9 x$

Factor $y$ out of $y (10 x) + y \cdot - 3$ .

$y (10 x - 3) = - 9 x$

Divide each term in $y (10 x - 3) = - 9 x$ by $10 x - 3$ and simplify.

Divide each term in $y (10 x - 3) = - 9 x$ by $10 x - 3$ .

$\frac{y (10 x - 3)}{10 x - 3} = \frac{- 9 x}{10 x - 3}$

Simplify the left side.

Cancel the common factor of $10 x - 3$ .

Cancel the common factor.

$\frac{y (10 x - 3)}{10 x - 3} = \frac{- 9 x}{10 x - 3}$

Divide $y$ by $1$ .

$y = \frac{- 9 x}{10 x - 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{9 x}{10 x - 3}$

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 9x+10xy=3y

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