Determine if Linear 11x+6xy=7y

$11 x + 6 x y = 7 y$

Step 1

Solve the equation for $y$ .

Subtract $7 y$ from both sides of the equation.

$11 x + 6 x y - 7 y = 0$

Subtract $11 x$ from both sides of the equation.

$6 x y - 7 y = - 11 x$

Factor $y$ out of $6 x y - 7 y$ .

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

$y (6 x) - 7 y = - 11 x$

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

$y (6 x) + y \cdot - 7 = - 11 x$

Factor $y$ out of $y (6 x) + y \cdot - 7$ .

$y (6 x - 7) = - 11 x$

Divide each term in $y (6 x - 7) = - 11 x$ by $6 x - 7$ and simplify.

Divide each term in $y (6 x - 7) = - 11 x$ by $6 x - 7$ .

$\frac{y (6 x - 7)}{6 x - 7} = \frac{- 11 x}{6 x - 7}$

Simplify the left side.

Cancel the common factor of $6 x - 7$ .

Cancel the common factor.

$\frac{y (6 x - 7)}{6 x - 7} = \frac{- 11 x}{6 x - 7}$

Divide $y$ by $1$ .

$y = \frac{- 11 x}{6 x - 7}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{11 x}{6 x - 7}$

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 11x+6xy=7y

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