Algebra Examples

$x = \frac{2}{y}$

Step 1

Rewrite the equation as $\frac{2}{y} = x$ .

$\frac{2}{y} = x$

Step 2

Find the LCD of the terms in the equation.

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

$y, 1$

The LCM of one and any expression is the expression.

$y$

Step 3

Multiply each term in $\frac{2}{y} = x$ by $y$ to eliminate the fractions.

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Multiply each term in $\frac{2}{y} = x$ by $y$ .

$\frac{2}{y} y = x y$

Simplify the left side.

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Cancel the common factor of $y$ .

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Cancel the common factor.

$\frac{2}{y} y = x y$

Rewrite the expression.

$2 = x y$

Step 4

Solve the equation.

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Rewrite the equation as $x y = 2$ .

$x y = 2$

Divide each term in $x y = 2$ by $x$ and simplify.

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Divide each term in $x y = 2$ by $x$ .

$\frac{x y}{x} = \frac{2}{x}$

Simplify the left side.

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Cancel the common factor of $x$ .

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Cancel the common factor.

$\frac{x y}{x} = \frac{2}{x}$

Divide $y$ by $1$ .

$y = \frac{2}{x}$

Step 5

The given equation $y = \frac{2}{x}$ can not be written as $y = k x$ , so $y$ doesn't vary directly with $x$ .

$y$ doesn't vary directly with $x$