Finite Math Examples

$3 x - 4 y = - 18$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

$- 4 y = - 18 - 3 x$

Step 1.2

Divide each term in $- 4 y = - 18 - 3 x$ by $- 4$ and simplify.

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Step 1.2.1

Divide each term in $- 4 y = - 18 - 3 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 18}{- 4} + \frac{- 3 x}{- 4}$

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.

$\frac{- 4 y}{- 4} = \frac{- 18}{- 4} + \frac{- 3 x}{- 4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 18}{- 4} + \frac{- 3 x}{- 4}$

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

Cancel the common factor of $- 18$ and $- 4$ .

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Step 1.2.3.1.1.1

Factor $- 2$ out of $- 18$ .

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

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $- 2$ out of $- 4$ .

$y = \frac{- 2 \cdot 9}{- 2 \cdot 2} + \frac{- 3 x}{- 4}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{- 2 \cdot 9}{- 2 \cdot 2} + \frac{- 3 x}{- 4}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

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

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{9}{2} + \frac{3 x}{4}$

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.

$y = \frac{9}{2} + \frac{3 (0)}{4}$

Step 3.2

Simplify $\frac{9}{2} + \frac{3 (0)}{4}$ .

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Step 3.2.1

Multiply $3$ by $0$ .

$y = \frac{9}{2} + \frac{0}{4}$

Step 3.2.2

Divide $0$ by $4$ .

$y = \frac{9}{2} + 0$

Step 3.2.3

Add $\frac{9}{2}$ and $0$ .

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

Step 3.3

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

$(0, \frac{9}{2})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{9}{2} + \frac{3 (1)}{4}$

Step 4.2

Simplify $\frac{9}{2} + \frac{3 (1)}{4}$ .

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Step 4.2.1

Multiply $3$ by $1$ .

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

Step 4.2.2

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{9}{2} \cdot \frac{2}{2} + \frac{3}{4}$

Step 4.2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.3.1

Multiply $\frac{9}{2}$ by $\frac{2}{2}$ .

$y = \frac{9 \cdot 2}{2 \cdot 2} + \frac{3}{4}$

Step 4.2.3.2

Multiply $2$ by $2$ .

$y = \frac{9 \cdot 2}{4} + \frac{3}{4}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{9 \cdot 2 + 3}{4}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $9$ by $2$ .

$y = \frac{18 + 3}{4}$

Step 4.2.5.2

Add $18$ and $3$ .

$y = \frac{21}{4}$

Step 4.3

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

$(1, \frac{21}{4})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Multiply $3$ by $2$ .

$y = \frac{9}{2} + \frac{6}{4}$

Step 5.2.2

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

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Step 5.2.2.1

Factor $2$ out of $6$ .

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

Step 5.2.2.2

Cancel the common factors.

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Step 5.2.2.2.1

Factor $2$ out of $4$ .

$y = \frac{9}{2} + \frac{2 \cdot 3}{2 \cdot 2}$

Step 5.2.2.2.2

Cancel the common factor.

$y = \frac{9}{2} + \frac{2 \cdot 3}{2 \cdot 2}$

Step 5.2.2.2.3

Rewrite the expression.

$y = \frac{9}{2} + \frac{3}{2}$

Step 5.2.3

Combine the numerators over the common denominator.

$y = \frac{9 + 3}{2}$

Step 5.2.4

Simplify the expression.

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Step 5.2.4.1

Add $9$ and $3$ .

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

Step 5.2.4.2

Divide $12$ by $2$ .

$y = 6$

Step 5.3

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

$(2, 6)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{9}{2}), (1, \frac{21}{4}), (2, 6)$

Step 7