Linear Algebra Examples

$\frac{1}{4} x - y = 6$

Step 1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - y = 6$

Step 2

Subtract $\frac{x}{4}$ from both sides of the equation.

$- y = 6 - \frac{x}{4}$

Step 3

Divide each term in $- y = 6 - \frac{x}{4}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = 6 - \frac{x}{4}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{6}{- 1} + \frac{- \frac{x}{4}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{6}{- 1} + \frac{- \frac{x}{4}}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{6}{- 1} + \frac{- \frac{x}{4}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $6$ by $- 1$ .

$y = - 6 + \frac{- \frac{x}{4}}{- 1}$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$y = - 6 + \frac{\frac{x}{4}}{1}$

Step 3.3.1.3

Divide $\frac{x}{4}$ by $1$ .

$y = - 6 + \frac{x}{4}$

Step 4

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 5