Linear Algebra Examples

$x - 5 y = 19$

Step 1

Subtract $x$ from both sides of the equation.

$- 5 y = 19 - x$

Step 2

Divide each term in $- 5 y = 19 - x$ by $- 5$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $- 5 y = 19 - x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{19}{- 5} + \frac{- x}{- 5}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{19}{- 5} + \frac{- x}{- 5}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{19}{- 5} + \frac{- x}{- 5}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{19}{5} + \frac{- x}{- 5}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{19}{5} + \frac{x}{5}$

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:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4