Linear Algebra Examples

2 x + 8 y = - 6

$2 x + 8 y = - 6$

Step 1

Subtract

$2 x$ from both sides of the equation.

$8 y = - 6 - 2 x$

Step 2

Divide each term in

$8 y = - 6 - 2 x$ by

$8$ and simplify.

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Step 2.1

Divide each term in

$8 y = - 6 - 2 x$ by

$8$ .

$\frac{8 y}{8} = \frac{- 6}{8} + \frac{- 2 x}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

$8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{- 6}{8} + \frac{- 2 x}{8}$

Step 2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{- 6}{8} + \frac{- 2 x}{8}$

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

Cancel the common factor of

$- 6$ and

$8$ .

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Step 2.3.1.1.1

Factor

$2$ out of

$- 6$ .

$y = \frac{2 (- 3)}{8} + \frac{- 2 x}{8}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor

$2$ out of

$8$ .

$y = \frac{2 \cdot - 3}{2 \cdot 4} + \frac{- 2 x}{8}$

Step 2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot - 3}{2 \cdot 4} + \frac{- 2 x}{8}$

Step 2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 3}{4} + \frac{- 2 x}{8}$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{3}{4} + \frac{- 2 x}{8}$

Step 2.3.1.3

Cancel the common factor of

$- 2$ and

$8$ .

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Step 2.3.1.3.1

Factor

$2$ out of

$- 2 x$ .

$y = - \frac{3}{4} + \frac{2 (- x)}{8}$

Step 2.3.1.3.2

Cancel the common factors.

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Step 2.3.1.3.2.1

Factor

$2$ out of

$8$ .

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

Step 2.3.1.3.2.2

Cancel the common factor.

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

Step 2.3.1.3.2.3

Rewrite the expression.

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

Step 2.3.1.4

Move the negative in front of the fraction.

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

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