Linear Algebra Examples

$7 - \frac{1}{3} y = 3 x$

Step 1

Rewrite the equation as $3 x = 7 - \frac{1}{3} y$ .

$3 x = 7 - \frac{1}{3} y$

Step 2

Divide each term in $3 x = 7 - \frac{1}{3} y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x = 7 - \frac{1}{3} y$ by $3$ .

$\frac{3 x}{3} = \frac{7}{3} + \frac{- \frac{1}{3} y}{3}$

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.

$\frac{3 x}{3} = \frac{7}{3} + \frac{- \frac{1}{3} y}{3}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{3} + \frac{- \frac{1}{3} y}{3}$

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

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

$x = \frac{7}{3} + \frac{- \frac{y}{3}}{3}$

Step 2.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{7}{3} - \frac{y}{3} \cdot \frac{1}{3}$

Step 2.3.1.3

Multiply $- \frac{y}{3} \cdot \frac{1}{3}$ .

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Step 2.3.1.3.1

Multiply $\frac{1}{3}$ by $\frac{y}{3}$ .

$x = \frac{7}{3} - \frac{y}{3 \cdot 3}$

Step 2.3.1.3.2

Multiply $3$ by $3$ .

$x = \frac{7}{3} - \frac{y}{9}$