Determine if Linear 2x+12xy=5y

$2 x + 12 x y = 5 y$

Step 1

Solve the equation for $y$ .

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

$2 x + 12 x y - 5 y = 0$

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

$12 x y - 5 y = - 2 x$

Factor $y$ out of $12 x y - 5 y$ .

Factor $y$ out of $12 x y$ .

$y (12 x) - 5 y = - 2 x$

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

$y (12 x) + y \cdot - 5 = - 2 x$

Factor $y$ out of $y (12 x) + y \cdot - 5$ .

$y (12 x - 5) = - 2 x$

Divide each term in $y (12 x - 5) = - 2 x$ by $12 x - 5$ and simplify.

Divide each term in $y (12 x - 5) = - 2 x$ by $12 x - 5$ .

$\frac{y (12 x - 5)}{12 x - 5} = \frac{- 2 x}{12 x - 5}$

Simplify the left side.

Cancel the common factor of $12 x - 5$ .

Cancel the common factor.

$\frac{y (12 x - 5)}{12 x - 5} = \frac{- 2 x}{12 x - 5}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{12 x - 5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{2 x}{12 x - 5}$

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 2x+12xy=5y

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