Finite Math Examples

$c = 5 x + 7 y$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $5 x + 7 y = c$ .

$5 x + 7 y = c$

Step 1.2

Subtract $5 x$ from both sides of the equation.

$7 y = c - 5 x$

Step 1.3

Divide each term in $7 y = c - 5 x$ by $7$ and simplify.

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Step 1.3.1

Divide each term in $7 y = c - 5 x$ by $7$ .

$\frac{7 y}{7} = \frac{c}{7} + \frac{- 5 x}{7}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $7$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{c}{7} + \frac{- 5 x}{7}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{c}{7} + \frac{- 5 x}{7}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$y = \frac{c}{7} - \frac{5 x}{7}$

Step 2

Choose any values for $x$ and $y$ that are in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ and $1$ to substitute for $z$ .

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Step 3.1

Remove parentheses.

$y = \frac{c}{7} - \frac{5 (0)}{7}$

Step 3.2

Simplify $\frac{c}{7} - \frac{5 (0)}{7}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{c - 5 \cdot 0}{7}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $- 5$ by $0$ .

$y = \frac{c + 0}{7}$

Step 3.2.2.2

Add $c$ and $0$ .

$y = \frac{c}{7}$

Step 3.3

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

$(0, \frac{c}{7}, 1)$

Step 4

Choose $1$ to substitute in for $x$ and $2$ to substitute for $z$ .

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Step 4.1

Remove parentheses.

$y = \frac{c}{7} - \frac{5 (1)}{7}$

Step 4.2

Multiply $5$ by $1$ .

$y = \frac{c}{7} - \frac{5}{7}$

Step 4.3

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

$(1, \frac{c}{7} - \frac{5}{7}, 2)$

Step 5

Choose $2$ to substitute in for $x$ and $3$ to substitute for $z$ .

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Step 5.1

Remove parentheses.

$y = \frac{c}{7} - \frac{5 (2)}{7}$

Step 5.2

Multiply $5$ by $2$ .

$y = \frac{c}{7} - \frac{10}{7}$

Step 5.3

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

$(2, \frac{c}{7} - \frac{10}{7}, 3)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{c}{7}, 1), (1, \frac{c}{7} - \frac{5}{7}, 2), (2, \frac{c}{7} - \frac{10}{7}, 3)$