Linear Algebra Examples

$5 x - 3 y = 6$

Step 1

Subtract $5 x$ from both sides of the equation.

$- 3 y = 6 - 5 x$

Step 2

Divide each term in $- 3 y = 6 - 5 x$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 y = 6 - 5 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{6}{- 3} + \frac{- 5 x}{- 3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{6}{- 3} + \frac{- 5 x}{- 3}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{- 3} + \frac{- 5 x}{- 3}$

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

Divide $6$ by $- 3$ .

$y = - 2 + \frac{- 5 x}{- 3}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = - 2 + \frac{5 x}{3}$

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