Pre-Algebra Examples

$- \frac{1}{2} x - y = 5$

Step 1

Solve the equation for $y$ .

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Step 1.1

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} - y = 5$

Step 1.2

Add $\frac{x}{2}$ to both sides of the equation.

$- y = 5 + \frac{x}{2}$

Step 1.3

Divide each term in $- y = 5 + \frac{x}{2}$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- y = 5 + \frac{x}{2}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{5}{- 1} + \frac{\frac{x}{2}}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{5}{- 1} + \frac{\frac{x}{2}}{- 1}$

Step 1.3.2.2

Divide $y$ by $1$ .

$y = \frac{5}{- 1} + \frac{\frac{x}{2}}{- 1}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $5$ by $- 1$ .

$y = - 5 + \frac{\frac{x}{2}}{- 1}$

Step 1.3.3.1.2

Move the negative one from the denominator of $\frac{\frac{x}{2}}{- 1}$ .

$y = - 5 - 1 \cdot \frac{x}{2}$

Step 1.3.3.1.3

Rewrite $- 1 \cdot \frac{x}{2}$ as $- \frac{x}{2}$ .

$y = - 5 - \frac{x}{2}$

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.

$y = - 5 - \frac{0}{2}$

Step 3.2

Simplify $- 5 - \frac{0}{2}$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Divide $0$ by $2$ .

$y = - 5 - 0$

Step 3.2.1.2

Multiply $- 1$ by $0$ .

$y = - 5 + 0$

Step 3.2.2

Add $- 5$ and $0$ .

$y = - 5$

Step 3.3

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

$(0, - 5)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - 5 - \frac{1}{2}$

Step 4.2

Simplify $- 5 - \frac{1}{2}$ .

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Step 4.2.1

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - 5 \cdot \frac{2}{2} - \frac{1}{2}$

Step 4.2.2

Combine $- 5$ and $\frac{2}{2}$ .

$y = \frac{- 5 \cdot 2}{2} - \frac{1}{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$y = \frac{- 5 \cdot 2 - 1}{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $- 5$ by $2$ .

$y = \frac{- 10 - 1}{2}$

Step 4.2.4.2

Subtract $1$ from $- 10$ .

$y = \frac{- 11}{2}$

Step 4.2.5

Move the negative in front of the fraction.

$y = - \frac{11}{2}$

Step 4.3

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

$(1, - \frac{11}{2})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - 5 - \frac{2}{2}$

Step 5.2

Simplify $- 5 - \frac{2}{2}$ .

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Cancel the common factor.

$y = - 5 - \frac{2}{2}$

Step 5.2.1.1.2

Rewrite the expression.

$y = - 5 - 1 \cdot 1$

Step 5.2.1.2

Multiply $- 1$ by $1$ .

$y = - 5 - 1$

Step 5.2.2

Subtract $1$ from $- 5$ .

$y = - 6$

Step 5.3

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

$(2, - 6)$

Step 6

These are three possible solutions to the equation.

$(0, - 5), (1, - \frac{11}{2}), (2, - 6)$

Step 7