Determine if Linear 3x+7xy=2y

$3 x + 7 x y = 2 y$

Step 1

Solve the equation for $y$ .

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

$3 x + 7 x y - 2 y = 0$

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

$7 x y - 2 y = - 3 x$

Factor $y$ out of $7 x y - 2 y$ .

Factor $y$ out of $7 x y$ .

$y (7 x) - 2 y = - 3 x$

Factor $y$ out of $- 2 y$ .

$y (7 x) + y \cdot - 2 = - 3 x$

Factor $y$ out of $y (7 x) + y \cdot - 2$ .

$y (7 x - 2) = - 3 x$

Divide each term in $y (7 x - 2) = - 3 x$ by $7 x - 2$ and simplify.

Divide each term in $y (7 x - 2) = - 3 x$ by $7 x - 2$ .

$\frac{y (7 x - 2)}{7 x - 2} = \frac{- 3 x}{7 x - 2}$

Simplify the left side.

Cancel the common factor of $7 x - 2$ .

Cancel the common factor.

$\frac{y (7 x - 2)}{7 x - 2} = \frac{- 3 x}{7 x - 2}$

Divide $y$ by $1$ .

$y = \frac{- 3 x}{7 x - 2}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{3 x}{7 x - 2}$

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 3x+7xy=2y

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