Linear Algebra Examples

x - 2 y = 2

$x - 2 y = 2$

Step 1

Subtract

x

$x$ from both sides of the equation.

- 2 y = 2 - x

$- 2 y = 2 - x$

Step 2

Divide each term in

- 2 y = 2 - x

$- 2 y = 2 - x$ by

- 2

$- 2$ and simplify.

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Step 2.1

Divide each term in

- 2 y = 2 - x

$- 2 y = 2 - x$ by

- 2

$- 2$ .

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

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

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{2}{- 2} + \frac{- x}{- 2}

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

Step 2.2.1.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

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

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

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

2

$2$ by

- 2

$- 2$ .

y = - 1 + \frac{- x}{- 2}

$y = - 1 + \frac{- x}{- 2}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

y = - 1 + \frac{x}{2}

$y = - 1 + \frac{x}{2}$

y = - 1 + \frac{x}{2}

$y = - 1 + \frac{x}{2}$

y = - 1 + \frac{x}{2}

$y = - 1 + \frac{x}{2}$

y = - 1 + \frac{x}{2}

$y = - 1 + \frac{x}{2}$

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)

$(- \infty, \infty)$

Set-Builder Notation:

{x | x \in ℝ}

${x | x \in ℝ}$

Step 4