Solve by Addition/Elimination -6x+6y=6 , -6x+3y=-12

$- 6 x + 6 y = 6$ , $- 6 x + 3 y = - 12$

Step 1

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

$(- 1) \cdot (- 6 x + 6 y) = (- 1) (6)$

$- 6 x + 3 y = - 12$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (- 6 x + 6 y)$ .

Apply the distributive property.

$- 1 (- 6 x) - 1 (6 y) = (- 1) (6)$

$- 6 x + 3 y = - 12$

Multiply.

Multiply $- 6$ by $- 1$ .

$6 x - 1 (6 y) = (- 1) (6)$

$- 6 x + 3 y = - 12$

Multiply $6$ by $- 1$ .

$6 x - 6 y = (- 1) (6)$

$- 6 x + 3 y = - 12$

$6 x - 6 y = (- 1) (6)$

$- 6 x + 3 y = - 12$

$6 x - 6 y = (- 1) (6)$

$- 6 x + 3 y = - 12$

$6 x - 6 y = (- 1) (6)$

$- 6 x + 3 y = - 12$

Simplify the right side.

Multiply $- 1$ by $6$ .

$6 x - 6 y = - 6$

$- 6 x + 3 y = - 12$

$6 x - 6 y = - 6$

$- 6 x + 3 y = - 12$

$6 x - 6 y = - 6$

$- 6 x + 3 y = - 12$

Step 3

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

		$6$	$x$	$-$	$6$	$y$	$=$		$-$	$6$
$+$	$-$	$6$	$x$	$+$	$3$	$y$	$=$	$-$	$1$	$2$
				$-$	$3$	$y$	$=$	$-$	$1$	$8$

Step 4

Divide each term in $- 3 y = - 18$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 18$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 18}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 18}{- 3}$

Simplify the right side.

Divide $- 18$ by $- 3$ .

$y = 6$

Step 5

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$6 x - 6 \cdot 6 = - 6$

Multiply $- 6$ by $6$ .

$6 x - 36 = - 6$

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

Add $36$ to both sides of the equation.

$6 x = - 6 + 36$

Add $- 6$ and $36$ .

$6 x = 30$

Divide each term in $6 x = 30$ by $6$ and simplify.

Divide each term in $6 x = 30$ by $6$ .

$\frac{6 x}{6} = \frac{30}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{30}{6}$

Divide $x$ by $1$ .

$x = \frac{30}{6}$

Simplify the right side.

Divide $30$ by $6$ .

$x = 5$

Step 6

The solution to the independent system of equations can be represented as a point.

$(5, 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(5, 6)$

Equation Form:

$x = 5, y = 6$

Step 8

Solve by Addition/Elimination -6x+6y=6 , -6x+3y=-12

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