Linear Algebra Examples

$3 x + \frac{1}{3} y = 21$

Step 1

Combine $\frac{1}{3}$ and $y$ .

$3 x + \frac{y}{3} = 21$

Step 2

Subtract $3 x$ from both sides of the equation.

$\frac{y}{3} = 21 - 3 x$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 (21 - 3 x)$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{y}{3} = 3 (21 - 3 x)$

Step 4.1.1.2

Rewrite the expression.

$y = 3 (21 - 3 x)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $3 (21 - 3 x)$ .

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Step 4.2.1.1

Apply the distributive property.

$y = 3 \cdot 21 + 3 (- 3 x)$

Step 4.2.1.2

Multiply.

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Step 4.2.1.2.1

Multiply $3$ by $21$ .

$y = 63 + 3 (- 3 x)$

Step 4.2.1.2.2

Multiply $- 3$ by $3$ .

$y = 63 - 9 x$

Step 5

Reorder $63$ and $- 9 x$ .

$y = - 9 x + 63$

Step 6

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 7