Algebra Examples

$x - 3 y = 9$ , $- x + 3 y = - 9$

Step 1

Add the two equations together to eliminate $x$ from the system.

		$x$	$-$	$3$	$y$	$=$		$9$
$+$	$-$	$x$	$+$	$3$	$y$	$=$	$-$	$9$
					$0$	$=$		$0$

Step 2

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Step 3

Solve one of the equations for $y$ .

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Step 3.1

Subtract $x$ from both sides of the equation.

$- 3 y = 9 - x$

Step 3.2

Divide each term in $- 3 y = 9 - x$ by $- 3$ and simplify.

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Step 3.2.1

Divide each term in $- 3 y = 9 - x$ by $- 3$ .

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Divide $9$ by $- 3$ .

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

Step 3.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 4

The solution is the set of ordered pairs that make $y = - 3 + \frac{x}{3}$ true.

$(x, - 3 + \frac{x}{3})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(x, - 3 + \frac{x}{3})$

Equation Form:

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

Step 6