Algebra Examples

$- v + w = 7$ $v + w = 1$

Step 1

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

	$-$	$v$	$+$	$w$	$=$	$7$
$+$		$v$	$+$	$w$	$=$	$1$
			$2$	$w$	$=$	$8$

Step 2

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

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Step 2.1

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

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

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.

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

Step 2.2.1.2

Divide $w$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $8$ by $2$ .

$w = 4$

Step 3

Substitute the value found for $w$ into one of the original equations, then solve for $v$ .

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Step 3.1

Substitute the value found for $w$ into one of the original equations to solve for $v$ .

$- v + 4 = 7$

Step 3.2

Move all terms not containing $v$ to the right side of the equation.

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$- v = 7 - 4$

Step 3.2.2

Subtract $4$ from $7$ .

$- v = 3$

Step 3.3

Divide each term in $- v = 3$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- v = 3$ by $- 1$ .

$\frac{- v}{- 1} = \frac{3}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{v}{1} = \frac{3}{- 1}$

Step 3.3.2.2

Divide $v$ by $1$ .

$v = \frac{3}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $3$ by $- 1$ .

$v = - 3$

Step 4

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

$w = 4$

$v = - 3$