Finite Math Examples

$4 x - 3 y = - 9$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $4 x$ from both sides of the equation.

$- 3 y = - 9 - 4 x$

Step 1.2

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

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Step 1.2.1

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

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

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.

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

Step 1.2.2.1.2

Divide $y$ by $1$ .

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

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 $- 9$ by $- 3$ .

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

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

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

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.

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

Step 3.2

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

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Step 3.2.1

Multiply $4$ by $0$ .

$y = 3 + \frac{0}{3}$

Step 3.2.2

Divide $0$ by $3$ .

$y = 3 + 0$

Step 3.2.3

Add $3$ and $0$ .

$y = 3$

Step 3.3

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

$(0, 3)$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Multiply $4$ by $1$ .

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

Step 4.2.2

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

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

Step 4.2.3

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

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

Step 4.2.4

Combine the numerators over the common denominator.

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

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $3$ by $3$ .

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

Step 4.2.5.2

Add $9$ and $4$ .

$y = \frac{13}{3}$

Step 4.3

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

$(1, \frac{13}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Multiply $4$ by $2$ .

$y = 3 + \frac{8}{3}$

Step 5.2.2

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

$y = 3 \cdot \frac{3}{3} + \frac{8}{3}$

Step 5.2.3

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

$y = \frac{3 \cdot 3}{3} + \frac{8}{3}$

Step 5.2.4

Combine the numerators over the common denominator.

$y = \frac{3 \cdot 3 + 8}{3}$

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $3$ by $3$ .

$y = \frac{9 + 8}{3}$

Step 5.2.5.2

Add $9$ and $8$ .

$y = \frac{17}{3}$

Step 5.3

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

$(2, \frac{17}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 3), (1, \frac{13}{3}), (2, \frac{17}{3})$

Step 7