Linear Algebra Examples

$6 x - 36 y = 36$

Step 1

Subtract $6 x$ from both sides of the equation.

$- 36 y = 36 - 6 x$

Step 2

Divide each term in $- 36 y = 36 - 6 x$ by $- 36$ and simplify.

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Step 2.1

Divide each term in $- 36 y = 36 - 6 x$ by $- 36$ .

$\frac{- 36 y}{- 36} = \frac{36}{- 36} + \frac{- 6 x}{- 36}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 36$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 36 y}{- 36} = \frac{36}{- 36} + \frac{- 6 x}{- 36}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{36}{- 36} + \frac{- 6 x}{- 36}$

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 $36$ by $- 36$ .

$y = - 1 + \frac{- 6 x}{- 36}$

Step 2.3.1.2

Cancel the common factor of $- 6$ and $- 36$ .

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Step 2.3.1.2.1

Factor $- 6$ out of $- 6 x$ .

$y = - 1 + \frac{- 6 (x)}{- 36}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $- 6$ out of $- 36$ .

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

Step 2.3.1.2.2.2

Cancel the common factor.

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

Step 2.3.1.2.2.3

Rewrite the expression.

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

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