Linear Algebra Examples

$3 x - y = 6$

Step 1

Subtract

$3 x$ from both sides of the equation.

$- y = 6 - 3 x$

Step 2

Divide each term in

$- y = 6 - 3 x$ by

$- 1$ and simplify.

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Step 2.1

Divide each term in

$- y = 6 - 3 x$ by

$- 1$ .

$\frac{- y}{- 1} = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Step 2.2.2

Divide

$y$ by

$1$ .

$y = \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide

$6$ by

$- 1$ .

$y = - 6 + \frac{- 3 x}{- 1}$

Step 2.3.1.2

Move the negative one from the denominator of

$\frac{- 3 x}{- 1}$ .

$y = - 6 - 1 \cdot (- 3 x)$

Step 2.3.1.3

Rewrite

$- 1 \cdot (- 3 x)$ as

$- (- 3 x)$ .

$y = - 6 - (- 3 x)$

Step 2.3.1.4

Multiply

$- 3$ by

$- 1$ .

$y = - 6 + 3 x$

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:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4