Linear Algebra Examples

$2 x - 2 y = 4$

Step 1

Subtract $2 x$ from both sides of the equation.

$- 2 y = 4 - 2 x$

Step 2

Divide each term in $- 2 y = 4 - 2 x$ by $- 2$ and simplify.

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Divide each term in $- 2 y = 4 - 2 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{4}{- 2} + \frac{- 2 x}{- 2}$

Simplify the left side.

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Cancel the common factor of $- 2$ .

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Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{4}{- 2} + \frac{- 2 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{4}{- 2} + \frac{- 2 x}{- 2}$

Simplify the right side.

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Simplify each term.

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Divide $4$ by $- 2$ .

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

Cancel the common factor of $- 2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

$y = - 2 + x$

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