Linear Algebra Examples

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

Step 1

Subtract $\frac{x}{3}$ from both sides of the equation.

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

Step 2

Multiply both sides of the equation by $- 6$ .

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 6 (- \frac{y}{6})$ .

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Step 3.1.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{y}{6}$ into the numerator.

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

Step 3.1.1.1.2

Factor $6$ out of $- 6$ .

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

Step 3.1.1.1.3

Cancel the common factor.

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

Step 3.1.1.1.4

Rewrite the expression.

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

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.1.2.2

Multiply $y$ by $1$ .

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 6 (1 - \frac{x}{3})$ .

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Step 3.2.1.1

Apply the distributive property.

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

Step 3.2.1.2

Multiply $- 6$ by $1$ .

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

Step 3.2.1.3

Cancel the common factor of $3$ .

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Step 3.2.1.3.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

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

Step 3.2.1.3.2

Factor $3$ out of $- 6$ .

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

Step 3.2.1.3.3

Cancel the common factor.

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

Step 3.2.1.3.4

Rewrite the expression.

$y = - 6 - 2 (- x)$

Step 3.2.1.4

Multiply $- 1$ by $- 2$ .

$y = - 6 + 2 x$

Step 4

Reorder $- 6$ and $2 x$ .

$y = 2 x - 6$

Step 5

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 6