Pre-Algebra Examples

$x - 4 y = 8$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $x$ from both sides of the equation.

$- 4 y = 8 - x$

Step 1.2

Divide each term in $- 4 y = 8 - x$ by $- 4$ and simplify.

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Step 1.2.1

Divide each term in $- 4 y = 8 - x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- x}{- 4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- x}{- 4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{- 4} + \frac{- x}{- 4}$

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 $8$ by $- 4$ .

$y = - 2 + \frac{- x}{- 4}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - 2 + \frac{x}{4}$

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.

$y = - 2 + \frac{0}{4}$

Step 3.2

Simplify $- 2 + \frac{0}{4}$ .

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Step 3.2.1

Divide $0$ by $4$ .

$y = - 2 + 0$

Step 3.2.2

Add $- 2$ and $0$ .

$y = - 2$

Step 3.3

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

$(0, - 2)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - 2 + \frac{1}{4}$

Step 4.2

Simplify $- 2 + \frac{1}{4}$ .

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Step 4.2.1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - 2 \cdot \frac{4}{4} + \frac{1}{4}$

Step 4.2.2

Combine $- 2$ and $\frac{4}{4}$ .

$y = \frac{- 2 \cdot 4}{4} + \frac{1}{4}$

Step 4.2.3

Combine the numerators over the common denominator.

$y = \frac{- 2 \cdot 4 + 1}{4}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $- 2$ by $4$ .

$y = \frac{- 8 + 1}{4}$

Step 4.2.4.2

Add $- 8$ and $1$ .

$y = \frac{- 7}{4}$

Step 4.2.5

Move the negative in front of the fraction.

$y = - \frac{7}{4}$

Step 4.3

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

$(1, - \frac{7}{4})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - 2 + \frac{2}{4}$

Step 5.2

Simplify $- 2 + \frac{2}{4}$ .

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Step 5.2.1

Cancel the common factor of $2$ and $4$ .

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Step 5.2.1.1

Factor $2$ out of $2$ .

$y = - 2 + \frac{2 (1)}{4}$

Step 5.2.1.2

Cancel the common factors.

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Step 5.2.1.2.1

Factor $2$ out of $4$ .

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

Step 5.2.1.2.2

Cancel the common factor.

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

Step 5.2.1.2.3

Rewrite the expression.

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

Step 5.2.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 5.2.3

Combine $- 2$ and $\frac{2}{2}$ .

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

Step 5.2.4

Combine the numerators over the common denominator.

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

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $- 2$ by $2$ .

$y = \frac{- 4 + 1}{2}$

Step 5.2.5.2

Add $- 4$ and $1$ .

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

Step 5.2.6

Move the negative in front of the fraction.

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

Step 5.3

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

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

Step 6

These are three possible solutions to the equation.

$(0, - 2), (1, - \frac{7}{4}), (2, - \frac{3}{2})$

Step 7