Solve by Addition/Elimination 2x-2y=-8 , x+2y=-1

$2 x - 2 y = - 8$ , $x + 2 y = - 1$

Step 1

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

$2 x - 2 y = - 8$

$(- 2) \cdot (x + 2 y) = (- 2) (- 1)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (x + 2 y)$ .

Apply the distributive property.

$2 x - 2 y = - 8$

$- 2 x - 2 (2 y) = (- 2) (- 1)$

Multiply $2$ by $- 2$ .

$2 x - 2 y = - 8$

$- 2 x - 4 y = (- 2) (- 1)$

$2 x - 2 y = - 8$

$- 2 x - 4 y = (- 2) (- 1)$

$2 x - 2 y = - 8$

$- 2 x - 4 y = (- 2) (- 1)$

Simplify the right side.

Multiply $- 2$ by $- 1$ .

$2 x - 2 y = - 8$

$- 2 x - 4 y = 2$

$2 x - 2 y = - 8$

$- 2 x - 4 y = 2$

$2 x - 2 y = - 8$

$- 2 x - 4 y = 2$

Step 3

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

		$2$	$x$	$-$	$2$	$y$	$=$	$-$	$8$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$		$2$
				$-$	$6$	$y$	$=$	$-$	$6$

Step 4

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

Divide each term in $- 6 y = - 6$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 6}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 6}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 6}$

Simplify the right side.

Divide $- 6$ by $- 6$ .

$y = 1$

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 $x$ .

$2 x - 2 \cdot 1 = - 8$

Multiply $- 2$ by $1$ .

$2 x - 2 = - 8$

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

Add $2$ to both sides of the equation.

$2 x = - 8 + 2$

Add $- 8$ and $2$ .

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

Step 6

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

$(- 3, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 3, 1)$

Equation Form:

$x = - 3, y = 1$

Step 8

Solve by Addition/Elimination 2x-2y=-8 , x+2y=-1

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