Finite Math Examples

$x - z + 3 y = 4$ , $z = 3 y$ , $y - x = 5 z$

Step 1

When three variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other two vary. The formula for direct variation is $y = k x z^{2}$ , where $k$ is the constant of variation.

$y = k x z^{2}$

Step 2

Solve the equation for $k$ , the constant of variation.

$k = \frac{y}{x z^{2}}$

Step 3

Replace the variables $x$ , $y$ , and $z$ with the actual values.

$k = \frac{5 z}{(4) \cdot {(3 y)}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $3 y$ .

$k = \frac{5 z}{4 \cdot (3^{2} y^{2})}$

Step 4.2

Raise $3$ to the power of $2$ .

$k = \frac{5 z}{4 \cdot (9 y^{2})}$

Step 4.3

Multiply $4$ by $9$ .

$k = \frac{5 z}{36 y^{2}}$

Step 5

Write the equation of variation such that $y = k x z^{2}$ , replacing $k$ with the $\frac{5 z}{36 y^{2}}$ .

$y = \frac{5 x z^{3}}{36 y^{2}}$