Pre-Algebra Examples

$x + 3 y = 6$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $x$ from both sides of the equation.

$3 y = 6 - x$

Step 1.2

Divide each term in $3 y = 6 - x$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 y = 6 - x$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3} + \frac{- x}{3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3} + \frac{- x}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{3} + \frac{- x}{3}$

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 $3$ .

$y = 2 + \frac{- x}{3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = 2 - \frac{x}{3}$

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.

$y = 2 - \frac{0}{3}$

Step 3.2

Simplify $2 - \frac{0}{3}$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Divide $0$ by $3$ .

$y = 2 - 0$

Step 3.2.1.2

Multiply $- 1$ by $0$ .

$y = 2 + 0$

Step 3.2.2

Add $2$ and $0$ .

$y = 2$

Step 3.3

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

$(0, 2)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = 2 - \frac{1}{3}$

Step 4.2

Simplify $2 - \frac{1}{3}$ .

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Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 2 \cdot \frac{3}{3} - \frac{1}{3}$

Step 4.2.2

Combine $2$ and $\frac{3}{3}$ .

$y = \frac{2 \cdot 3}{3} - \frac{1}{3}$

Step 4.2.3

Combine the numerators over the common denominator.

$y = \frac{2 \cdot 3 - 1}{3}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $2$ by $3$ .

$y = \frac{6 - 1}{3}$

Step 4.2.4.2

Subtract $1$ from $6$ .

$y = \frac{5}{3}$

Step 4.3

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

$(1, \frac{5}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = 2 - \frac{2}{3}$

Step 5.2

Simplify $2 - \frac{2}{3}$ .

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Step 5.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 2 \cdot \frac{3}{3} - \frac{2}{3}$

Step 5.2.2

Combine $2$ and $\frac{3}{3}$ .

$y = \frac{2 \cdot 3}{3} - \frac{2}{3}$

Step 5.2.3

Combine the numerators over the common denominator.

$y = \frac{2 \cdot 3 - 2}{3}$

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $2$ by $3$ .

$y = \frac{6 - 2}{3}$

Step 5.2.4.2

Subtract $2$ from $6$ .

$y = \frac{4}{3}$

Step 5.3

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

$(2, \frac{4}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 2), (1, \frac{5}{3}), (2, \frac{4}{3})$

Step 7