Finite Math Examples

$4 x + 16 y = 460$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

$16 y = 460 - 4 x$

Step 1.2

Divide each term in $16 y = 460 - 4 x$ by $16$ and simplify.

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Step 1.2.1

Divide each term in $16 y = 460 - 4 x$ by $16$ .

$\frac{16 y}{16} = \frac{460}{16} + \frac{- 4 x}{16}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $16$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{16 y}{16} = \frac{460}{16} + \frac{- 4 x}{16}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{460}{16} + \frac{- 4 x}{16}$

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 $460$ and $16$ .

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Step 1.2.3.1.1.1

Factor $4$ out of $460$ .

$y = \frac{4 (115)}{16} + \frac{- 4 x}{16}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $4$ out of $16$ .

$y = \frac{4 \cdot 115}{4 \cdot 4} + \frac{- 4 x}{16}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{4 \cdot 115}{4 \cdot 4} + \frac{- 4 x}{16}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{115}{4} + \frac{- 4 x}{16}$

Step 1.2.3.1.2

Cancel the common factor of $- 4$ and $16$ .

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Step 1.2.3.1.2.1

Factor $4$ out of $- 4 x$ .

$y = \frac{115}{4} + \frac{4 (- x)}{16}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $4$ out of $16$ .

$y = \frac{115}{4} + \frac{4 (- x)}{4 (4)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{115}{4} + \frac{4 (- x)}{4 \cdot 4}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{115}{4} + \frac{- x}{4}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y = \frac{115}{4} - \frac{x}{4}$

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.

$y = \frac{115}{4} - \frac{0}{4}$

Step 3.2

Simplify $\frac{115}{4} - \frac{0}{4}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{115 + 0}{4}$

Step 3.2.2

Add $115$ and $0$ .

$y = \frac{115}{4}$

Step 3.3

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

$(0, \frac{115}{4})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{115}{4} - \frac{1}{4}$

Step 4.2

Simplify $\frac{115}{4} - \frac{1}{4}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{115 - 1}{4}$

Step 4.2.2

Subtract $1$ from $115$ .

$y = \frac{114}{4}$

Step 4.2.3

Cancel the common factor of $114$ and $4$ .

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Step 4.2.3.1

Factor $2$ out of $114$ .

$y = \frac{2 (57)}{4}$

Step 4.2.3.2

Cancel the common factors.

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Step 4.2.3.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 57}{2 \cdot 2}$

Step 4.2.3.2.2

Cancel the common factor.

$y = \frac{2 \cdot 57}{2 \cdot 2}$

Step 4.2.3.2.3

Rewrite the expression.

$y = \frac{57}{2}$

Step 4.3

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

$(1, \frac{57}{2})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{115}{4} - \frac{2}{4}$

Step 5.2

Simplify $\frac{115}{4} - \frac{2}{4}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{115 - 2}{4}$

Step 5.2.2

Subtract $2$ from $115$ .

$y = \frac{113}{4}$

Step 5.3

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

$(2, \frac{113}{4})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{115}{4}), (1, \frac{57}{2}), (2, \frac{113}{4})$

Step 7