Algebra Examples

$p + q = 0$ $q - p = 8$

Step 1

Simplify the left side.

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Step 1.1

Reorder $q$ and $- p$ .

$- p + q = 8$

$p + q = 0$

$- p + q = 8$

$p + q = 0$

Step 2

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

		$p$	$+$	$q$	$=$	$0$
$+$	$-$	$p$	$+$	$q$	$=$	$8$
			$2$	$q$	$=$	$8$

Step 3

Divide each term in $2 q = 8$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 q = 8$ by $2$ .

$\frac{2 q}{2} = \frac{8}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 q}{2} = \frac{8}{2}$

Step 3.2.1.2

Divide $q$ by $1$ .

$q = \frac{8}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $8$ by $2$ .

$q = 4$

Step 4

Substitute the value found for $q$ into one of the original equations, then solve for $p$ .

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Step 4.1

Substitute the value found for $q$ into one of the original equations to solve for $p$ .

$p + 4 = 0$

Step 4.2

Subtract $4$ from both sides of the equation.

$p = - 4$

Step 5

This is the final solution to the independent system of equations.

$q = 4$

$p = - 4$