Linear Algebra Examples

6 x - 2 y = 12

$6 x - 2 y = 12$

Step 1

Subtract

6 x

$6 x$ from both sides of the equation.

- 2 y = 12 - 6 x

$- 2 y = 12 - 6 x$

Step 2

Divide each term in

- 2 y = 12 - 6 x

$- 2 y = 12 - 6 x$ by

- 2

$- 2$ and simplify.

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Step 2.1

Divide each term in

- 2 y = 12 - 6 x

$- 2 y = 12 - 6 x$ by

- 2

$- 2$ .

\frac{- 2 y}{- 2} = \frac{12}{- 2} + \frac{- 6 x}{- 2}

$\frac{- 2 y}{- 2} = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

Step 2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

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

$12$ by

$- 2$ .

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

Step 2.3.1.2

Cancel the common factor of

$- 6$ and

$- 2$ .

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Step 2.3.1.2.1

Factor

$- 2$ out of

$- 6 x$ .

$y = - 6 + \frac{- 2 (3 x)}{- 2}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor

$- 2$ out of

$- 2$ .

$y = - 6 + \frac{- 2 (3 x)}{- 2 (1)}$

Step 2.3.1.2.2.2

Cancel the common factor.

$y = - 6 + \frac{- 2 (3 x)}{- 2 \cdot 1}$

Step 2.3.1.2.2.3

Rewrite the expression.

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

Step 2.3.1.2.2.4

Divide

$3 x$ 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