Finite Math Examples

$z = 0.2 x + 0.75 y$ , $z = 2.5 x + 0.25 y$

Step 1

Solve the equation for $x$ .

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Step 1.1

Rewrite the equation as $0.2 x + 0.75 y = z$ .

$0.2 x + 0.75 y = z$

$z = 2.5 x + 0.25 y$

Step 1.2

Subtract $0.75 y$ from both sides of the equation.

$0.2 x = z - 0.75 y$

$z = 2.5 x + 0.25 y$

Step 1.3

Divide each term in $0.2 x = z - 0.75 y$ by $0.2$ and simplify.

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Step 1.3.1

Divide each term in $0.2 x = z - 0.75 y$ by $0.2$ .

$\frac{0.2 x}{0.2} = \frac{z}{0.2} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $0.2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{0.2 x}{0.2} = \frac{z}{0.2} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{z}{0.2} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

$x = \frac{z}{0.2} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

$x = \frac{z}{0.2} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

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 $1$ .

$x = \frac{1 z}{0.2} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.2

Factor $0.2$ out of $0.2$ .

$x = \frac{1 z}{0.2 (1)} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.3

Separate fractions.

$x = \frac{1}{0.2} \cdot \frac{z}{1} + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.4

Divide $1$ by $0.2$ .

$x = 5 (\frac{z}{1}) + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.5

Divide $z$ by $1$ .

$x = 5 z + \frac{- 0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.6

Move the negative in front of the fraction.

$x = 5 z - \frac{0.75 y}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.7

Factor $0.75$ out of $0.75 y$ .

$x = 5 z - \frac{0.75 (y)}{0.2}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.8

Factor $0.2$ out of $0.2$ .

$x = 5 z - \frac{0.75 (y)}{0.2 (1)}$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.9

Separate fractions.

$x = 5 z - (\frac{0.75}{0.2} \cdot \frac{y}{1})$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.10

Divide $0.75$ by $0.2$ .

$x = 5 z - (3.75 (\frac{y}{1}))$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.11

Divide $y$ by $1$ .

$x = 5 z - (3.75 y)$

$z = 2.5 x + 0.25 y$

Step 1.3.3.1.12

Multiply $3.75$ by $- 1$ .

$x = 5 z - 3.75 y$

$z = 2.5 x + 0.25 y$

$x = 5 z - 3.75 y$

$z = 2.5 x + 0.25 y$

$x = 5 z - 3.75 y$

$z = 2.5 x + 0.25 y$

$x = 5 z - 3.75 y$

$z = 2.5 x + 0.25 y$

$x = 5 z - 3.75 y$

$z = 2.5 x + 0.25 y$

Step 2

Solve the equation for $y$ .

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Step 2.1

Rewrite the equation as $2.5 (5 z - 3.75 y) + 0.25 y = z$ .

$2.5 (5 z - 3.75 y) + 0.25 y = z$

$x = 5 z - 3.75 y$

Step 2.2

Simplify $2.5 (5 z - 3.75 y) + 0.25 y$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Apply the distributive property.

$2.5 (5 z) + 2.5 (- 3.75 y) + 0.25 y = z$

$x = 5 z - 3.75 y$

Step 2.2.1.2

Multiply $5$ by $2.5$ .

$12.5 z + 2.5 (- 3.75 y) + 0.25 y = z$

$x = 5 z - 3.75 y$

Step 2.2.1.3

Multiply $- 3.75$ by $2.5$ .

$12.5 z - 9.375 y + 0.25 y = z$

$x = 5 z - 3.75 y$

$12.5 z - 9.375 y + 0.25 y = z$

$x = 5 z - 3.75 y$

Step 2.2.2

Add $- 9.375 y$ and $0.25 y$ .

$12.5 z - 9.125 y = z$

$x = 5 z - 3.75 y$

$12.5 z - 9.125 y = z$

$x = 5 z - 3.75 y$

Step 2.3

Move all terms not containing $y$ to the right side of the equation.

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Step 2.3.1

Subtract $12.5 z$ from both sides of the equation.

$- 9.125 y = z - 12.5 z$

$x = 5 z - 3.75 y$

Step 2.3.2

Subtract $12.5 z$ from $z$ .

$- 9.125 y = - 11.5 z$

$x = 5 z - 3.75 y$

$- 9.125 y = - 11.5 z$

$x = 5 z - 3.75 y$

Step 2.4

Divide each term in $- 9.125 y = - 11.5 z$ by $- 9.125$ and simplify.

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Step 2.4.1

Divide each term in $- 9.125 y = - 11.5 z$ by $- 9.125$ .

$\frac{- 9.125 y}{- 9.125} = \frac{- 11.5 z}{- 9.125}$

$x = 5 z - 3.75 y$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 9.125$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 9.125 y}{- 9.125} = \frac{- 11.5 z}{- 9.125}$

$x = 5 z - 3.75 y$

Step 2.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 11.5 z}{- 9.125}$

$x = 5 z - 3.75 y$

$y = \frac{- 11.5 z}{- 9.125}$

$x = 5 z - 3.75 y$

$y = \frac{- 11.5 z}{- 9.125}$

$x = 5 z - 3.75 y$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Dividing two negative values results in a positive value.

$y = \frac{11.5 z}{9.125}$

$x = 5 z - 3.75 y$

Step 2.4.3.2

Factor $11.5$ out of $11.5 z$ .

$y = \frac{11.5 (z)}{9.125}$

$x = 5 z - 3.75 y$

Step 2.4.3.3

Factor $9.125$ out of $9.125$ .

$y = \frac{11.5 (z)}{9.125 (1)}$

$x = 5 z - 3.75 y$

Step 2.4.3.4

Separate fractions.

$y = \frac{11.5}{9.125} \cdot \frac{z}{1}$

$x = 5 z - 3.75 y$

Step 2.4.3.5

Divide $11.5$ by $9.125$ .

$y = 1.26027397 (\frac{z}{1})$

$x = 5 z - 3.75 y$

Step 2.4.3.6

Divide $z$ by $1$ .

$y = 1.26027397 z$

$x = 5 z - 3.75 y$

$y = 1.26027397 z$

$x = 5 z - 3.75 y$

$y = 1.26027397 z$

$x = 5 z - 3.75 y$

$y = 1.26027397 z$

$x = 5 z - 3.75 y$

Step 3

Simplify the right side.

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Step 3.1

Simplify $5 z - 3.75 (1.26027397 z)$ .

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Step 3.1.1

Multiply $1.26027397$ by $- 3.75$ .

$x = 5 z - 4.72602739 z$

$y = 1.26027397 z$

Step 3.1.2

Subtract $4.72602739 z$ from $5 z$ .

$x = 0.2739726 z$

$y = 1.26027397 z$

$x = 0.2739726 z$

$y = 1.26027397 z$

$x = 0.2739726 z$

$y = 1.26027397 z$