Finite Math Examples

$x = 10 x + 10 y$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $10 x + 10 y = x$ .

$10 x + 10 y = x$

Step 1.2

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

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

$10 y = x - 10 x$

Step 1.2.2

Subtract $10 x$ from $x$ .

$10 y = - 9 x$

Step 1.3

Divide each term in $10 y = - 9 x$ by $10$ and simplify.

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Step 1.3.1

Divide each term in $10 y = - 9 x$ by $10$ .

$\frac{10 y}{10} = \frac{- 9 x}{10}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $10$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{- 9 x}{10}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 9 x}{10}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$y = - \frac{9 x}{10}$

Step 2

Set $10 x + 10 y$ equal to $0$ .

$- \frac{9 x}{10} = 0$

Step 3

Solve for $x$ .

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Step 3.1

Set the numerator equal to zero.

$9 x = 0$

Step 3.2

Divide each term in $9 x = 0$ by $9$ and simplify.

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Step 3.2.1

Divide each term in $9 x = 0$ by $9$ .

$\frac{9 x}{9} = \frac{0}{9}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $9$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{0}{9}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{9}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $0$ by $9$ .

$x = 0$

Step 4