Linear Algebra Examples

3 x + 2 y = 6

$3 x + 2 y = 6$

Step 1

Subtract

3 x

$3 x$ from both sides of the equation.

2 y = 6 - 3 x

$2 y = 6 - 3 x$

Step 2

Divide each term in

2 y = 6 - 3 x

$2 y = 6 - 3 x$ by

2

$2$ and simplify.

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Step 2.1

Divide each term in

2 y = 6 - 3 x

$2 y = 6 - 3 x$ by

2

$2$ .

\frac{2 y}{2} = \frac{6}{2} + \frac{- 3 x}{2}

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 3 x}{2}$

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.

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 3 x}{2}$

Step 2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{6}{2} + \frac{- 3 x}{2}$

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

$6$ by

$2$ .

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

Step 2.3.1.2

Move the negative in front of the fraction.

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

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:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4

$3 x + 2 y = 6$

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