Algebra Examples

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

Step 1

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

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

$- x + 3 y = 6$

Step 2

Add $x$ to both sides of the equation.

$3 y = 6 + x$

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

Step 3

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

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Step 3.1

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

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

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

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

Step 3.2.1.2

Divide $y$ by $1$ .

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

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

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

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

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

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $6$ by $3$ .

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

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

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

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

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

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

Step 4

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

Always true

Step 5