Algebra Examples

$6 x + 2 x y = 10 y$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $10 y$ from both sides of the equation.

$6 x + 2 x y - 10 y = 0$

Step 1.2

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

$2 x y - 10 y = - 6 x$

Step 1.3

Factor $2 y$ out of $2 x y - 10 y$ .

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Step 1.3.1

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

$2 y (x) - 10 y = - 6 x$

Step 1.3.2

Factor $2 y$ out of $- 10 y$ .

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

Step 1.3.3

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $2$ .

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Step 1.4.2.1.1

Cancel the common factor.

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

Step 1.4.2.1.2

Rewrite the expression.

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

Step 1.4.2.2

Cancel the common factor of $x - 5$ .

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Step 1.4.2.2.1

Cancel the common factor.

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

Step 1.4.2.2.2

Divide $y$ by $1$ .

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

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Cancel the common factor of $- 6$ and $2$ .

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Step 1.4.3.1.1

Factor $2$ out of $- 6 x$ .

$y = \frac{2 (- 3 x)}{2 (x - 5)}$

Step 1.4.3.1.2

Cancel the common factors.

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Step 1.4.3.1.2.1

Cancel the common factor.

$y = \frac{2 (- 3 x)}{2 (x - 5)}$

Step 1.4.3.1.2.2

Rewrite the expression.

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

Step 1.4.3.2

Move the negative in front of the fraction.

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

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