Pre-Algebra Examples

$x - 2 y = 2$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $x$ from both sides of the equation.

$- 2 y = 2 - x$

Step 1.2

Divide each term in $- 2 y = 2 - x$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 y = 2 - x$ by $- 2$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $y$ by $1$ .

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

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 $2$ by $- 2$ .

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

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

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

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.

$y = - 1 + \frac{0}{2}$

Step 3.2

Simplify $- 1 + \frac{0}{2}$ .

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Step 3.2.1

Divide $0$ by $2$ .

$y = - 1 + 0$

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.

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

Step 4.2

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

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Step 4.2.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.2.2

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

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

Step 4.2.3

Combine the numerators over the common denominator.

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

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $- 1$ by $2$ .

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

Step 4.2.4.2

Add $- 2$ and $1$ .

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

Step 4.2.5

Move the negative in front of the fraction.

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

Step 4.3

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

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

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Divide $2$ by $2$ .

$y = - 1 + 1$

Step 5.2.2

Add $- 1$ and $1$ .

$y = 0$

Step 5.3

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

$(2, 0)$

Step 6

These are three possible solutions to the equation.

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

Step 7