Solve by Addition/Elimination x-2y=-12 x+6y=20

$x - 2 y = - 12$ $x + 6 y = 20$

Step 1

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

$x - 2 y = - 12$

$(- 1) \cdot (x + 6 y) = (- 1) (20)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$x - 2 y = - 12$

$- 1 x - 1 (6 y) = (- 1) (20)$

Simplify the expression.

Rewrite $- 1 x$ as $- x$ .

$x - 2 y = - 12$

$- x - 1 (6 y) = (- 1) (20)$

Multiply $6$ by $- 1$ .

$x - 2 y = - 12$

$- x - 6 y = (- 1) (20)$

$x - 2 y = - 12$

$- x - 6 y = (- 1) (20)$

$x - 2 y = - 12$

$- x - 6 y = (- 1) (20)$

$x - 2 y = - 12$

$- x - 6 y = (- 1) (20)$

Simplify the right side.

Multiply $- 1$ by $20$ .

$x - 2 y = - 12$

$- x - 6 y = - 20$

$x - 2 y = - 12$

$- x - 6 y = - 20$

$x - 2 y = - 12$

$- x - 6 y = - 20$

Step 3

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

		$x$	$-$	$2$	$y$	$=$	$-$	$1$	$2$
$+$	$-$	$x$	$-$	$6$	$y$	$=$	$-$	$2$	$0$
			$-$	$8$	$y$	$=$	$-$	$3$	$2$

Step 4

Divide each term in $- 8 y = - 32$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 32$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 32}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 32}{- 8}$

Divide $y$ by $1$ .

$y = \frac{- 32}{- 8}$

Simplify the right side.

Divide $- 32$ by $- 8$ .

$y = 4$

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 $x$ .

$x - 2 \cdot 4 = - 12$

Multiply $- 2$ by $4$ .

$x - 8 = - 12$

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

Add $8$ to both sides of the equation.

$x = - 12 + 8$

Add $- 12$ and $8$ .

$x = - 4$

Step 6

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

$(- 4, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 4, 4)$

Equation Form:

$x = - 4, y = 4$

Step 8

Solve by Addition/Elimination x-2y=-12 x+6y=20

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