Algebra Examples

$6 a + 6 b = 12$ $6 a - 5 b = 12$

Step 1

Multiply each equation by the value that makes the coefficients of $a$ opposite.

$(- 1) \cdot (6 a + 6 b) = (- 1) (12)$

$6 a - 5 b = 12$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(- 1) \cdot (6 a + 6 b)$ .

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Step 2.1.1.1

Apply the distributive property.

$- 1 (6 a) - 1 (6 b) = (- 1) (12)$

$6 a - 5 b = 12$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $6$ by $- 1$ .

$- 6 a - 1 (6 b) = (- 1) (12)$

$6 a - 5 b = 12$

Step 2.1.1.2.2

Multiply $6$ by $- 1$ .

$- 6 a - 6 b = (- 1) (12)$

$6 a - 5 b = 12$

$- 6 a - 6 b = (- 1) (12)$

$6 a - 5 b = 12$

$- 6 a - 6 b = (- 1) (12)$

$6 a - 5 b = 12$

$- 6 a - 6 b = (- 1) (12)$

$6 a - 5 b = 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 1$ by $12$ .

$- 6 a - 6 b = - 12$

$6 a - 5 b = 12$

$- 6 a - 6 b = - 12$

$6 a - 5 b = 12$

$- 6 a - 6 b = - 12$

$6 a - 5 b = 12$

Step 3

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

	$-$	$6$	$a$		$-$	$6$	$b$	$=$	$-$	$1$	$2$
$+$		$6$	$a$		$-$	$5$	$b$	$=$		$1$	$2$
				$-$	$1$	$1$	$b$	$=$			$0$

Step 4

Divide each term in $- 11 b = 0$ by $- 11$ and simplify.

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Step 4.1

Divide each term in $- 11 b = 0$ by $- 11$ .

$\frac{- 11 b}{- 11} = \frac{0}{- 11}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 11$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 11 b}{- 11} = \frac{0}{- 11}$

Step 4.2.1.2

Divide $b$ by $1$ .

$b = \frac{0}{- 11}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $- 11$ .

$b = 0$

Step 5

Substitute the value found for $b$ into one of the original equations, then solve for $a$ .

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Step 5.1

Substitute the value found for $b$ into one of the original equations to solve for $a$ .

$- 6 a - 6 \cdot 0 = - 12$

Step 5.2

Simplify $- 6 a - 6 \cdot 0$ .

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Step 5.2.1

Multiply $- 6$ by $0$ .

$- 6 a + 0 = - 12$

Step 5.2.2

Add $- 6 a$ and $0$ .

$- 6 a = - 12$

Step 5.3

Divide each term in $- 6 a = - 12$ by $- 6$ and simplify.

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Step 5.3.1

Divide each term in $- 6 a = - 12$ by $- 6$ .

$\frac{- 6 a}{- 6} = \frac{- 12}{- 6}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $- 6$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{- 6 a}{- 6} = \frac{- 12}{- 6}$

Step 5.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 12}{- 6}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $- 12$ by $- 6$ .

$a = 2$

Step 6

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

$b = 0$

$a = 2$

	$-$	$6$	$a$		$-$	$6$	$b$	$=$	$-$	$1$	$2$
$+$		$6$	$a$		$-$	$5$	$b$	$=$		$1$	$2$
				$-$	$1$	$1$	$b$	$=$			$0$

	$-$	$6$	$a$		$-$	$6$	$b$	$=$	$-$	$1$	$2$
$+$		$6$	$a$		$-$	$5$	$b$	$=$		$1$	$2$
				$-$	$1$	$1$	$b$	$=$			$0$

	$-$	$6$	$a$		$-$	$6$	$b$	$=$	$-$	$1$	$2$
$+$		$6$	$a$		$-$	$5$	$b$	$=$		$1$	$2$
				$-$	$1$	$1$	$b$	$=$			$0$