Pre-Algebra Examples

$3 x + 2 y = 12$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$2 y = 12 - 3 x$

Step 1.2

Divide each term in $2 y = 12 - 3 x$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y = 12 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{12}{2} + \frac{- 3 x}{2}$

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.

$\frac{2 y}{2} = \frac{12}{2} + \frac{- 3 x}{2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{2} + \frac{- 3 x}{2}$

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 $12$ by $2$ .

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

Step 1.2.3.1.2

Move the negative in front of the fraction.

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

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.

$y = 6 - \frac{3 (0)}{2}$

Step 3.2

Simplify $6 - \frac{3 (0)}{2}$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Cancel the common factor of $0$ and $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $3 (0)$ .

$y = 6 - \frac{2 (3 \cdot (0))}{2}$

Step 3.2.1.1.2

Cancel the common factors.

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Step 3.2.1.1.2.1

Factor $2$ out of $2$ .

$y = 6 - \frac{2 (3 \cdot (0))}{2 (1)}$

Step 3.2.1.1.2.2

Cancel the common factor.

$y = 6 - \frac{2 (3 \cdot (0))}{2 \cdot 1}$

Step 3.2.1.1.2.3

Rewrite the expression.

$y = 6 - \frac{3 \cdot (0)}{1}$

Step 3.2.1.1.2.4

Divide $3 \cdot (0)$ by $1$ .

$y = 6 - (3 \cdot (0))$

Step 3.2.1.2

Multiply $- (3 \cdot (0))$ .

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Step 3.2.1.2.1

Multiply $3$ by $0$ .

$y = 6 - 0$

Step 3.2.1.2.2

Multiply $- 1$ 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.

$y = 6 - \frac{3 (1)}{2}$

Step 4.2

Simplify $6 - \frac{3 (1)}{2}$ .

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Step 4.2.1

Multiply $3$ by $1$ .

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

Step 4.2.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.2.3

Combine $6$ and $\frac{2}{2}$ .

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

Step 4.2.4

Combine the numerators over the common denominator.

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

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $6$ by $2$ .

$y = \frac{12 - 3}{2}$

Step 4.2.5.2

Subtract $3$ from $12$ .

$y = \frac{9}{2}$

Step 4.3

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

$(1, \frac{9}{2})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

Simplify $6 - \frac{3 (2)}{2}$ .

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Cancel the common factor.

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

Step 5.2.1.1.2

Divide $3$ by $1$ .

$y = 6 - 1 \cdot 3$

Step 5.2.1.2

Multiply $- 1$ by $3$ .

$y = 6 - 3$

Step 5.2.2

Subtract $3$ from $6$ .

$y = 3$

Step 5.3

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

$(2, 3)$

Step 6

These are three possible solutions to the equation.

$(0, 6), (1, \frac{9}{2}), (2, 3)$

Step 7