Finite Math Examples

$z = 6 x + 2 y$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $6 x + 2 y = z$ .

$6 x + 2 y = z$

Step 1.2

Subtract $6 x$ from both sides of the equation.

$2 y = z - 6 x$

Step 1.3

Divide each term in $2 y = z - 6 x$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 y = z - 6 x$ by $2$ .

$\frac{2 y}{2} = \frac{z}{2} + \frac{- 6 x}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{z}{2} + \frac{- 6 x}{2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{z}{2} + \frac{- 6 x}{2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Cancel the common factor of $- 6$ and $2$ .

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Step 1.3.3.1.1

Factor $2$ out of $- 6 x$ .

$y = \frac{z}{2} + \frac{2 (- 3 x)}{2}$

Step 1.3.3.1.2

Cancel the common factors.

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Step 1.3.3.1.2.1

Factor $2$ out of $2$ .

$y = \frac{z}{2} + \frac{2 (- 3 x)}{2 (1)}$

Step 1.3.3.1.2.2

Cancel the common factor.

$y = \frac{z}{2} + \frac{2 (- 3 x)}{2 \cdot 1}$

Step 1.3.3.1.2.3

Rewrite the expression.

$y = \frac{z}{2} + \frac{- 3 x}{1}$

Step 1.3.3.1.2.4

Divide $- 3 x$ by $1$ .

$y = \frac{z}{2} - 3 x$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ , the degree of variable $z$ is $1$ and the degree of variable $x$ is $1$ .

Linear