Pre-Algebra Examples

$3 x - 4 y = 9$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

$- 4 y = 9 - 3 x$

Step 1.2

Divide each term in $- 4 y = 9 - 3 x$ by $- 4$ and simplify.

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Step 1.2.1

Divide each term in $- 4 y = 9 - 3 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{9}{- 4} + \frac{- 3 x}{- 4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{9}{- 4} + \frac{- 3 x}{- 4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{9}{- 4} + \frac{- 3 x}{- 4}$

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

Move the negative in front of the fraction.

$y = - \frac{9}{4} + \frac{- 3 x}{- 4}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{9}{4} + \frac{3 x}{4}$

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.

$y = - \frac{9}{4} + \frac{3 (0)}{4}$

Step 3.2

Simplify $- \frac{9}{4} + \frac{3 (0)}{4}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 9 + 3 (0)}{4}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $3$ by $0$ .

$y = \frac{- 9 + 0}{4}$

Step 3.2.2.2

Add $- 9$ and $0$ .

$y = \frac{- 9}{4}$

Step 3.2.2.3

Move the negative in front of the fraction.

$y = - \frac{9}{4}$

Step 3.3

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

$(0, - \frac{9}{4})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - \frac{9}{4} + \frac{3 (1)}{4}$

Step 4.2

Simplify $- \frac{9}{4} + \frac{3 (1)}{4}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 9 + 3 (1)}{4}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $3$ by $1$ .

$y = \frac{- 9 + 3}{4}$

Step 4.2.2.2

Add $- 9$ and $3$ .

$y = \frac{- 6}{4}$

Step 4.2.3

Cancel the common factor of $- 6$ and $4$ .

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Step 4.2.3.1

Factor $2$ out of $- 6$ .

$y = \frac{2 (- 3)}{4}$

Step 4.2.3.2

Cancel the common factors.

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Step 4.2.3.2.1

Factor $2$ out of $4$ .

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

Step 4.2.3.2.2

Cancel the common factor.

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

Step 4.2.3.2.3

Rewrite the expression.

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

Step 4.2.4

Move the negative in front of the fraction.

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

Step 4.3

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

$(1, - \frac{3}{2})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - \frac{9}{4} + \frac{3 (2)}{4}$

Step 5.2

Simplify $- \frac{9}{4} + \frac{3 (2)}{4}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 9 + 3 (2)}{4}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $3$ by $2$ .

$y = \frac{- 9 + 6}{4}$

Step 5.2.2.2

Add $- 9$ and $6$ .

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

Step 5.2.2.3

Move the negative in front of the fraction.

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

Step 5.3

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

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

Step 6

These are three possible solutions to the equation.

$(0, - \frac{9}{4}), (1, - \frac{3}{2}), (2, - \frac{3}{4})$

Step 7