Linear Algebra Examples

6 x - 5 y = 10

$6 x - 5 y = 10$

Step 1

Subtract

6 x

$6 x$ from both sides of the equation.

- 5 y = 10 - 6 x

$- 5 y = 10 - 6 x$

Step 2

Divide each term in

- 5 y = 10 - 6 x

$- 5 y = 10 - 6 x$ by

- 5

$- 5$ and simplify.

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Step 2.1

Divide each term in

- 5 y = 10 - 6 x

$- 5 y = 10 - 6 x$ by

- 5

$- 5$ .

\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 6 x}{- 5}

$\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 6 x}{- 5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

- 5

$- 5$ .

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Step 2.2.1.1

Cancel the common factor.

\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 6 x}{- 5}

$\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 6 x}{- 5}$

Step 2.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{10}{- 5} + \frac{- 6 x}{- 5}

$y = \frac{10}{- 5} + \frac{- 6 x}{- 5}$

y = \frac{10}{- 5} + \frac{- 6 x}{- 5}

$y = \frac{10}{- 5} + \frac{- 6 x}{- 5}$

y = \frac{10}{- 5} + \frac{- 6 x}{- 5}

$y = \frac{10}{- 5} + \frac{- 6 x}{- 5}$

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

10

$10$ by

- 5

$- 5$ .

y = - 2 + \frac{- 6 x}{- 5}

$y = - 2 + \frac{- 6 x}{- 5}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

y = - 2 + \frac{6 x}{5}

$y = - 2 + \frac{6 x}{5}$

y = - 2 + \frac{6 x}{5}

$y = - 2 + \frac{6 x}{5}$

y = - 2 + \frac{6 x}{5}

$y = - 2 + \frac{6 x}{5}$

y = - 2 + \frac{6 x}{5}

$y = - 2 + \frac{6 x}{5}$

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