Finite Math Examples

$z = 0.039 x + 0.029 y$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $0.039 x + 0.029 y = z$ .

$0.039 x + 0.029 y = z$

Step 1.2

Subtract $0.039 x$ from both sides of the equation.

$0.029 y = z - 0.039 x$

Step 1.3

Divide each term in $0.029 y = z - 0.039 x$ by $0.029$ and simplify.

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Step 1.3.1

Divide each term in $0.029 y = z - 0.039 x$ by $0.029$ .

$\frac{0.029 y}{0.029} = \frac{z}{0.029} + \frac{- 0.039 x}{0.029}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $0.029$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{0.029 y}{0.029} = \frac{z}{0.029} + \frac{- 0.039 x}{0.029}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{z}{0.029} + \frac{- 0.039 x}{0.029}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Multiply by $1$ .

$y = \frac{1 z}{0.029} + \frac{- 0.039 x}{0.029}$

Step 1.3.3.1.2

Factor $0.029$ out of $0.029$ .

$y = \frac{1 z}{0.029 (1)} + \frac{- 0.039 x}{0.029}$

Step 1.3.3.1.3

Separate fractions.

$y = \frac{1}{0.029} \cdot \frac{z}{1} + \frac{- 0.039 x}{0.029}$

Step 1.3.3.1.4

Divide $1$ by $0.029$ .

$y = 34.48275862 \frac{z}{1} + \frac{- 0.039 x}{0.029}$

Step 1.3.3.1.5

Divide $z$ by $1$ .

$y = 34.48275862 z + \frac{- 0.039 x}{0.029}$

Step 1.3.3.1.6

Move the negative in front of the fraction.

$y = 34.48275862 z - \frac{0.039 x}{0.029}$

Step 1.3.3.1.7

Factor $0.039$ out of $0.039 x$ .

$y = 34.48275862 z - \frac{0.039 (x)}{0.029}$

Step 1.3.3.1.8

Factor $0.029$ out of $0.029$ .

$y = 34.48275862 z - \frac{0.039 (x)}{0.029 (1)}$

Step 1.3.3.1.9

Separate fractions.

$y = 34.48275862 z - (\frac{0.039}{0.029} \cdot \frac{x}{1})$

Step 1.3.3.1.10

Divide $0.039$ by $0.029$ .

$y = 34.48275862 z - (1.34482758 \frac{x}{1})$

Step 1.3.3.1.11

Divide $x$ by $1$ .

$y = 34.48275862 z - (1.34482758 x)$

Step 1.3.3.1.12

Multiply $1.34482758$ by $- 1$ .

$y = 34.48275862 z - 1.34482758 x$

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.

$y = 34.48275862 (1) - 1.34482758 \cdot 0$

Step 3.2

Simplify $34.48275862 (1) - 1.34482758 \cdot 0$ .

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Multiply $34.48275862$ by $1$ .

$y = 34.48275862 - 1.34482758 \cdot 0$

Step 3.2.1.2

Multiply $- 1.34482758$ by $0$ .

$y = 34.48275862 + 0$

Step 3.2.2

Add $34.48275862$ and $0$ .

$y = 34.48275862$

Step 3.3

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

$(0, 34.48275862, 1)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = 34.48275862 (2) - 1.34482758 \cdot 1$

Step 4.2

Simplify $34.48275862 (2) - 1.34482758 \cdot 1$ .

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $34.48275862$ by $2$ .

$y = 68.96551724 - 1.34482758 \cdot 1$

Step 4.2.1.2

Multiply $- 1.34482758$ by $1$ .

$y = 68.96551724 - 1.34482758$

Step 4.2.2

Subtract $1.34482758$ from $68.96551724$ .

$y = 67.62068965$

Step 4.3

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

$(1, 67.62068965, 2)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = 34.48275862 (3) - 1.34482758 \cdot 2$

Step 5.2

Simplify $34.48275862 (3) - 1.34482758 \cdot 2$ .

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Multiply $34.48275862$ by $3$ .

$y = 103.44827586 - 1.34482758 \cdot 2$

Step 5.2.1.2

Multiply $- 1.34482758$ by $2$ .

$y = 103.44827586 - 2.68965517$

Step 5.2.2

Subtract $2.68965517$ from $103.44827586$ .

$y = 100.75862068$

Step 5.3

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

$(2, 100.75862068, 3)$

Step 6

These are three possible solutions to the equation.

$(0, 34.48275862, 1), (1, 67.62068965, 2), (2, 100.75862068, 3)$