Pre-Algebra Examples

3 x - y = 13

$3 x - y = 13$

Step 1

Solve the equation for

y

$y$ .

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Step 1.1

Subtract

3 x

$3 x$ from both sides of the equation.

- y = 13 - 3 x

$- y = 13 - 3 x$

Step 1.2

Divide each term in

- y = 13 - 3 x

$- y = 13 - 3 x$ by

- 1

$- 1$ and simplify.

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Step 1.2.1

Divide each term in

- y = 13 - 3 x

$- y = 13 - 3 x$ by

- 1

$- 1$ .

\frac{- y}{- 1} = \frac{13}{- 1} + \frac{- 3 x}{- 1}

$\frac{- y}{- 1} = \frac{13}{- 1} + \frac{- 3 x}{- 1}$

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{13}{- 1} + \frac{- 3 x}{- 1}

$\frac{y}{1} = \frac{13}{- 1} + \frac{- 3 x}{- 1}$

Step 1.2.2.2

Divide

y

$y$ by

1

$1$ .

y = \frac{13}{- 1} + \frac{- 3 x}{- 1}

$y = \frac{13}{- 1} + \frac{- 3 x}{- 1}$

y = \frac{13}{- 1} + \frac{- 3 x}{- 1}

$y = \frac{13}{- 1} + \frac{- 3 x}{- 1}$

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

13

$13$ by

- 1

$- 1$ .

y = - 13 + \frac{- 3 x}{- 1}

$y = - 13 + \frac{- 3 x}{- 1}$

Step 1.2.3.1.2

Move the negative one from the denominator of

\frac{- 3 x}{- 1}

$\frac{- 3 x}{- 1}$ .

y = - 13 - 1 \cdot (- 3 x)

$y = - 13 - 1 \cdot (- 3 x)$

Step 1.2.3.1.3

Rewrite

- 1 \cdot (- 3 x)

$- 1 \cdot (- 3 x)$ as

- (- 3 x)

$- (- 3 x)$ .

y = - 13 - (- 3 x)

$y = - 13 - (- 3 x)$

Step 1.2.3.1.4

Multiply

- 3

$- 3$ by

- 1

$- 1$ .

y = - 13 + 3 x

$y = - 13 + 3 x$

y = - 13 + 3 x

$y = - 13 + 3 x$

y = - 13 + 3 x

$y = - 13 + 3 x$

y = - 13 + 3 x

$y = - 13 + 3 x$

y = - 13 + 3 x

$y = - 13 + 3 x$

Step 2

Choose any value for

x

$x$ that is in the domain to plug into the equation.

Step 3

Choose

0

$0$ to substitute in for

x

$x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

y = - 13 + 3 (0)

$y = - 13 + 3 (0)$

Step 3.2

Simplify

- 13 + 3 (0)

$- 13 + 3 (0)$ .

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Step 3.2.1

Multiply

3

$3$ by

0

$0$ .

y = - 13 + 0

$y = - 13 + 0$

Step 3.2.2

Add

- 13

$- 13$ and

0

$0$ .

y = - 13

$y = - 13$

y = - 13

$y = - 13$

Step 3.3

Use the

x

$x$ and

y

$y$ values to form the ordered pair.

(0, - 13)

$(0, - 13)$

(0, - 13)

$(0, - 13)$

Step 4

Choose

1

$1$ to substitute in for

x

$x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

y = - 13 + 3 (1)

$y = - 13 + 3 (1)$

Step 4.2

Simplify

- 13 + 3 (1)

$- 13 + 3 (1)$ .

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Step 4.2.1

Multiply

3

$3$ by

1

$1$ .

y = - 13 + 3

$y = - 13 + 3$

Step 4.2.2

Add

- 13

$- 13$ and

3

$3$ .

y = - 10

$y = - 10$

y = - 10

$y = - 10$

Step 4.3

Use the

x

$x$ and

y

$y$ values to form the ordered pair.

(1, - 10)

$(1, - 10)$

(1, - 10)

$(1, - 10)$

Step 5

Choose

2

$2$ to substitute in for

x

$x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

y = - 13 + 3 (2)

$y = - 13 + 3 (2)$

Step 5.2

Simplify

- 13 + 3 (2)

$- 13 + 3 (2)$ .

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Step 5.2.1

Multiply

3

$3$ by

2

$2$ .

y = - 13 + 6

$y = - 13 + 6$

Step 5.2.2

Add

- 13

$- 13$ and

6

$6$ .

y = - 7

$y = - 7$

y = - 7

$y = - 7$

Step 5.3

Use the

x

$x$ and

y

$y$ values to form the ordered pair.

(2, - 7)

$(2, - 7)$

(2, - 7)

$(2, - 7)$

Step 6

These are three possible solutions to the equation.

(0, - 13), (1, - 10), (2, - 7)

$(0, - 13), (1, - 10), (2, - 7)$

Step 7