Precalculus Examples

$y = \frac{1}{3} x + 3$ , $2 y = \frac{2}{3} x + 6$

Step 1

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

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

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

Step 2

Divide each term in $2 y = \frac{2}{3} x + 6$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 y = \frac{2}{3} x + 6$ by $2$ .

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

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

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

Step 2.2.1.2

Divide $y$ by $1$ .

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

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

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

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

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

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

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 $\frac{2}{3}$ and $x$ .

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

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

Step 2.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{2 x}{3} \cdot \frac{1}{2} + \frac{6}{2}$

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

Step 2.3.1.3

Cancel the common factor of $2$ .

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Step 2.3.1.3.1

Factor $2$ out of $2 x$ .

$y = \frac{2 (x)}{3} \cdot \frac{1}{2} + \frac{6}{2}$

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

Step 2.3.1.3.2

Cancel the common factor.

$y = \frac{2 x}{3} \cdot \frac{1}{2} + \frac{6}{2}$

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

Step 2.3.1.3.3

Rewrite the expression.

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

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

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

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

Step 2.3.1.4

Divide $6$ by $2$ .

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

Step 3

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

Step 4

Nothing further can be done with this topic. Please check the expression entered or try another topic.

$y = \frac{1}{3} x + 3, 2 y = \frac{2}{3} x + 6$

Step 5