Linear Algebra Examples

$\frac{x}{3} - \frac{y}{8} = 1$

Step 1

Subtract $\frac{x}{3}$ from both sides of the equation.

$- \frac{y}{8} = 1 - \frac{x}{3}$

Step 2

Multiply both sides of the equation by $- 8$ .

$- 8 (- \frac{y}{8}) = - 8 (1 - \frac{x}{3})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 8 (- \frac{y}{8})$ .

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Step 3.1.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{y}{8}$ into the numerator.

$- 8 \frac{- y}{8} = - 8 (1 - \frac{x}{3})$

Step 3.1.1.1.2

Factor $8$ out of $- 8$ .

$8 (- 1) \frac{- y}{8} = - 8 (1 - \frac{x}{3})$

Step 3.1.1.1.3

Cancel the common factor.

$8 \cdot - 1 \frac{- y}{8} = - 8 (1 - \frac{x}{3})$

Step 3.1.1.1.4

Rewrite the expression.

$- - y = - 8 (1 - \frac{x}{3})$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 8 (1 - \frac{x}{3})$

Step 3.1.1.2.2

Multiply $y$ by $1$ .

$y = - 8 (1 - \frac{x}{3})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 8 (1 - \frac{x}{3})$ .

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Step 3.2.1.1

Apply the distributive property.

$y = - 8 \cdot 1 - 8 (- \frac{x}{3})$

Step 3.2.1.2

Multiply $- 8$ by $1$ .

$y = - 8 - 8 (- \frac{x}{3})$

Step 3.2.1.3

Multiply $- 8 (- \frac{x}{3})$ .

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Step 3.2.1.3.1

Multiply $- 1$ by $- 8$ .

$y = - 8 + 8 \frac{x}{3}$

Step 3.2.1.3.2

Combine $8$ and $\frac{x}{3}$ .

$y = - 8 + \frac{8 x}{3}$

Step 4

Reorder $- 8$ and $\frac{8 x}{3}$ .

$y = \frac{8 x}{3} - 8$

Step 5

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 6