Finite Math Examples

$\frac{1}{3} x + \frac{1}{3} y = - 1$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + \frac{1}{3} y = - 1$

Step 1.2

Combine $\frac{1}{3}$ and $y$ .

$\frac{x}{3} + \frac{y}{3} = - 1$

Step 2

Subtract $\frac{y}{3}$ from both sides of the equation.

$\frac{x}{3} = - 1 - \frac{y}{3}$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (- 1 - \frac{y}{3})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 (- 1 - \frac{y}{3})$

Step 4.1.1.2

Rewrite the expression.

$x = 3 (- 1 - \frac{y}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $3 (- 1 - \frac{y}{3})$ .

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Step 4.2.1.1

Apply the distributive property.

$x = 3 \cdot - 1 + 3 (- \frac{y}{3})$

Step 4.2.1.2

Multiply $3$ by $- 1$ .

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

Step 4.2.1.3

Cancel the common factor of $3$ .

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Step 4.2.1.3.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

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

Step 4.2.1.3.2

Cancel the common factor.

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

Step 4.2.1.3.3

Rewrite the expression.

$x = - 3 - y$

Step 5

Reorder $- 3$ and $- y$ .

$x = - y - 3$