Pre-Algebra Examples

$x - 6 y = 6$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $x$ from both sides of the equation.

$- 6 y = 6 - x$

Step 1.2

Divide each term in $- 6 y = 6 - x$ by $- 6$ and simplify.

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Step 1.2.1

Divide each term in $- 6 y = 6 - x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{6}{- 6} + \frac{- x}{- 6}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 6$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{6}{- 6} + \frac{- x}{- 6}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{- 6} + \frac{- x}{- 6}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $6$ by $- 6$ .

$y = - 1 + \frac{- x}{- 6}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - 1 + \frac{x}{6}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = - 1 + \frac{0}{6}$

Step 3.2

Simplify $- 1 + \frac{0}{6}$ .

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Step 3.2.1

Divide $0$ by $6$ .

$y = - 1 + 0$

Step 3.2.2

Add $- 1$ and $0$ .

$y = - 1$

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, - 1)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - 1 + \frac{1}{6}$

Step 4.2

Simplify $- 1 + \frac{1}{6}$ .

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Step 4.2.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = - 1 \cdot \frac{6}{6} + \frac{1}{6}$

Step 4.2.2

Combine $- 1$ and $\frac{6}{6}$ .

$y = \frac{- 1 \cdot 6}{6} + \frac{1}{6}$

Step 4.2.3

Combine the numerators over the common denominator.

$y = \frac{- 1 \cdot 6 + 1}{6}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $- 1$ by $6$ .

$y = \frac{- 6 + 1}{6}$

Step 4.2.4.2

Add $- 6$ and $1$ .

$y = \frac{- 5}{6}$

Step 4.2.5

Move the negative in front of the fraction.

$y = - \frac{5}{6}$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{5}{6})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - 1 + \frac{2}{6}$

Step 5.2

Simplify $- 1 + \frac{2}{6}$ .

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Step 5.2.1

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

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Step 5.2.1.1

Factor $2$ out of $2$ .

$y = - 1 + \frac{2 (1)}{6}$

Step 5.2.1.2

Cancel the common factors.

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Step 5.2.1.2.1

Factor $2$ out of $6$ .

$y = - 1 + \frac{2 \cdot 1}{2 \cdot 3}$

Step 5.2.1.2.2

Cancel the common factor.

$y = - 1 + \frac{2 \cdot 1}{2 \cdot 3}$

Step 5.2.1.2.3

Rewrite the expression.

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

Step 5.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5.2.3

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

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

Step 5.2.4

Combine the numerators over the common denominator.

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

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $- 1$ by $3$ .

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

Step 5.2.5.2

Add $- 3$ and $1$ .

$y = \frac{- 2}{3}$

Step 5.2.6

Move the negative in front of the fraction.

$y = - \frac{2}{3}$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{2}{3})$

Step 6

These are three possible solutions to the equation.

$(0, - 1), (1, - \frac{5}{6}), (2, - \frac{2}{3})$

Step 7