Pre-Algebra Examples

$2 x - y = 6$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$- y = 6 - 2 x$

Step 1.2

Divide each term in $- y = 6 - 2 x$ by $- 1$ and simplify.

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Step 1.2.1

Divide each term in $- y = 6 - 2 x$ by $- 1$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.2.2

Divide $y$ by $1$ .

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

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 $- 1$ .

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

Step 1.2.3.1.2

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

$y = - 6 - 1 \cdot (- 2 x)$

Step 1.2.3.1.3

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y = - 6 - (- 2 x)$

Step 1.2.3.1.4

Multiply $- 2$ by $- 1$ .

$y = - 6 + 2 x$

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.

$y = - 6 + 2 (0)$

Step 3.2

Simplify $- 6 + 2 (0)$ .

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Step 3.2.1

Multiply $2$ by $0$ .

$y = - 6 + 0$

Step 3.2.2

Add $- 6$ and $0$ .

$y = - 6$

Step 3.3

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

$(0, - 6)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - 6 + 2 (1)$

Step 4.2

Simplify $- 6 + 2 (1)$ .

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Step 4.2.1

Multiply $2$ by $1$ .

$y = - 6 + 2$

Step 4.2.2

Add $- 6$ and $2$ .

$y = - 4$

Step 4.3

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

$(1, - 4)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - 6 + 2 (2)$

Step 5.2

Simplify $- 6 + 2 (2)$ .

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Step 5.2.1

Multiply $2$ by $2$ .

$y = - 6 + 4$

Step 5.2.2

Add $- 6$ and $4$ .

$y = - 2$

Step 5.3

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

$(2, - 2)$

Step 6

These are three possible solutions to the equation.

$(0, - 6), (1, - 4), (2, - 2)$

Step 7