Linear Algebra Examples

$3 x - 4 y = 12$

Step 1

Subtract

$3 x$ from both sides of the equation.

$- 4 y = 12 - 3 x$

Step 2

Divide each term in

$- 4 y = 12 - 3 x$ by

$- 4$ and simplify.

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Step 2.1

Divide each term in

$- 4 y = 12 - 3 x$ by

$- 4$ .

$\frac{- 4 y}{- 4} = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

$- 4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Step 2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

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

$12$ by

$- 4$ .

$y = - 3 + \frac{- 3 x}{- 4}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = - 3 + \frac{3 x}{4}$

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