Pre-Algebra Examples

$x = - y + 7$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $- y + 7 = x$ .

$- y + 7 = x$

Step 1.2

Subtract $7$ from both sides of the equation.

$- y = x - 7$

Step 1.3

Divide each term in $- y = x - 7$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- y = x - 7$ by $- 1$ .

$\frac{- y}{- 1} = \frac{x}{- 1} + \frac{- 7}{- 1}$

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.

$\frac{y}{1} = \frac{x}{- 1} + \frac{- 7}{- 1}$

Step 1.3.2.2

Divide $y$ by $1$ .

$y = \frac{x}{- 1} + \frac{- 7}{- 1}$

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

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

$y = - 1 \cdot x + \frac{- 7}{- 1}$

Step 1.3.3.1.2

Rewrite $- 1 \cdot x$ as $- x$ .

$y = - x + \frac{- 7}{- 1}$

Step 1.3.3.1.3

Divide $- 7$ by $- 1$ .

$y = - x + 7$

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.

$y = - (0) + 7$

Step 3.2

Simplify $- (0) + 7$ .

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Step 3.2.1

Multiply $- 1$ by $0$ .

$y = 0 + 7$

Step 3.2.2

Add $0$ and $7$ .

$y = 7$

Step 3.3

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

$(0, 7)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - (1) + 7$

Step 4.2

Simplify $- (1) + 7$ .

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Step 4.2.1

Multiply $- 1$ by $1$ .

$y = - 1 + 7$

Step 4.2.2

Add $- 1$ and $7$ .

$y = 6$

Step 4.3

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

$(1, 6)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - (2) + 7$

Step 5.2

Simplify $- (2) + 7$ .

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Step 5.2.1

Multiply $- 1$ by $2$ .

$y = - 2 + 7$

Step 5.2.2

Add $- 2$ and $7$ .

$y = 5$

Step 5.3

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

$(2, 5)$

Step 6

These are three possible solutions to the equation.

$(0, 7), (1, 6), (2, 5)$

Step 7