Algebra Examples

$x + \frac{5}{y} = 0$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $x$ from both sides of the equation.

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

Step 1.2

Find the LCD of the terms in the equation.

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Step 1.2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y, 1$

Step 1.2.2

The LCM of one and any expression is the expression.

$y$

Step 1.3

Multiply each term in $\frac{5}{y} = - x$ by $y$ to eliminate the fractions.

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Step 1.3.1

Multiply each term in $\frac{5}{y} = - x$ by $y$ .

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $y$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Rewrite the expression.

$5 = - x y$

Step 1.4

Solve the equation.

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Step 1.4.1

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

$- x y = 5$

Step 1.4.2

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

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Step 1.4.2.1

Divide each term in $- x y = 5$ by $- x$ .

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

Step 1.4.2.2

Simplify the left side.

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Step 1.4.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.4.2.2.2

Cancel the common factor of $x$ .

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Step 1.4.2.2.2.1

Cancel the common factor.

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

Step 1.4.2.2.2.2

Divide $y$ by $1$ .

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

Step 1.4.2.3

Simplify the right side.

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Step 1.4.2.3.1

Move the negative in front of the fraction.

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

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