Linear Algebra Examples

2 x - 3 y = 4

$2 x - 3 y = 4$

Step 1

Subtract

2 x

$2 x$ from both sides of the equation.

- 3 y = 4 - 2 x

$- 3 y = 4 - 2 x$

Step 2

Divide each term in

- 3 y = 4 - 2 x

$- 3 y = 4 - 2 x$ by

- 3

$- 3$ and simplify.

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Step 2.1

Divide each term in

- 3 y = 4 - 2 x

$- 3 y = 4 - 2 x$ by

- 3

$- 3$ .

\frac{- 3 y}{- 3} = \frac{4}{- 3} + \frac{- 2 x}{- 3}

$\frac{- 3 y}{- 3} = \frac{4}{- 3} + \frac{- 2 x}{- 3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{4}{- 3} + \frac{- 2 x}{- 3}$

Step 2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{4}{- 3} + \frac{- 2 x}{- 3}$

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

Move the negative in front of the fraction.

$y = - \frac{4}{3} + \frac{- 2 x}{- 3}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{4}{3} + \frac{2 x}{3}$

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