Finite Math Examples

$6 x + 5 x y = 2 y$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

$6 x + 5 x y - 2 y = 0$

Step 1.2

Subtract $6 x$ from both sides of the equation.

$5 x y - 2 y = - 6 x$

Step 1.3

Factor $y$ out of $5 x y - 2 y$ .

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Step 1.3.1

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

$y (5 x) - 2 y = - 6 x$

Step 1.3.2

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

$y (5 x) + y \cdot - 2 = - 6 x$

Step 1.3.3

Factor $y$ out of $y (5 x) + y \cdot - 2$ .

$y (5 x - 2) = - 6 x$

Step 1.4

Divide each term in $y (5 x - 2) = - 6 x$ by $5 x - 2$ and simplify.

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Step 1.4.1

Divide each term in $y (5 x - 2) = - 6 x$ by $5 x - 2$ .

$\frac{y (5 x - 2)}{5 x - 2} = \frac{- 6 x}{5 x - 2}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $5 x - 2$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{y (5 x - 2)}{5 x - 2} = \frac{- 6 x}{5 x - 2}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6 x}{5 x - 2}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Move the negative in front of the fraction.

$y = - \frac{6 x}{5 x - 2}$

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