Determine if Linear x=3xy-5

$x = 3 x y - 5$

Step 1

Solve the equation for $y$ .

Rewrite the equation as $3 x y - 5 = x$ .

$3 x y - 5 = x$

Add $5$ to both sides of the equation.

$3 x y = x + 5$

Divide each term in $3 x y = x + 5$ by $3 x$ and simplify.

Divide each term in $3 x y = x + 5$ by $3 x$ .

$\frac{3 x y}{3 x} = \frac{x}{3 x} + \frac{5}{3 x}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x y}{3 x} = \frac{x}{3 x} + \frac{5}{3 x}$

Rewrite the expression.

$\frac{x y}{x} = \frac{x}{3 x} + \frac{5}{3 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y}{x} = \frac{x}{3 x} + \frac{5}{3 x}$

Divide $y$ by $1$ .

$y = \frac{x}{3 x} + \frac{5}{3 x}$

Simplify the right side.

Cancel the common factor of $x$ .

Cancel the common factor.

$y = \frac{x}{3 x} + \frac{5}{3 x}$

Rewrite the expression.

$y = \frac{1}{3} + \frac{5}{3 x}$

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 x=3xy-5

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