Linear Algebra Examples

4 x - y = 0

$4 x - y = 0$

Step 1

Subtract

4 x

$4 x$ from both sides of the equation.

- y = - 4 x

$- y = - 4 x$

Step 2

Divide each term in

- y = - 4 x

$- y = - 4 x$ by

- 1

$- 1$ and simplify.

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Step 2.1

Divide each term in

- y = - 4 x

$- y = - 4 x$ by

- 1

$- 1$ .

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

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

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

Step 2.2.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of

\frac{- 4 x}{- 1}

$\frac{- 4 x}{- 1}$ .

y = - 1 \cdot (- 4 x)

$y = - 1 \cdot (- 4 x)$

Step 2.3.2

Rewrite

- 1 \cdot (- 4 x)

$- 1 \cdot (- 4 x)$ as

- (- 4 x)

$- (- 4 x)$ .

y = - (- 4 x)

$y = - (- 4 x)$

Step 2.3.3

Multiply

- 4

$- 4$ by

- 1

$- 1$ .

y = 4 x

$y = 4 x$

y = 4 x

$y = 4 x$

y = 4 x

$y = 4 x$

Step 3

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)

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4