Solve by Addition/Elimination x+2y=-6 3x+8y=-20

$x + 2 y = - 6$ $3 x + 8 y = - 20$

Step 1

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

$(- 3) \cdot (x + 2 y) = (- 3) (- 6)$

$3 x + 8 y = - 20$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (x + 2 y)$ .

Apply the distributive property.

$- 3 x - 3 (2 y) = (- 3) (- 6)$

$3 x + 8 y = - 20$

Multiply $2$ by $- 3$ .

$- 3 x - 6 y = (- 3) (- 6)$

$3 x + 8 y = - 20$

$- 3 x - 6 y = (- 3) (- 6)$

$3 x + 8 y = - 20$

$- 3 x - 6 y = (- 3) (- 6)$

$3 x + 8 y = - 20$

Simplify the right side.

Multiply $- 3$ by $- 6$ .

$- 3 x - 6 y = 18$

$3 x + 8 y = - 20$

$- 3 x - 6 y = 18$

$3 x + 8 y = - 20$

$- 3 x - 6 y = 18$

$3 x + 8 y = - 20$

Step 3

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

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

Step 4

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

Divide each term in $2 y = - 2$ by $2$ .

$\frac{2 y}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2}{2}$

Divide $y$ by $1$ .

$y = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$y = - 1$

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 $x$ .

$- 3 x - 6 \cdot - 1 = 18$

Multiply $- 6$ by $- 1$ .

$- 3 x + 6 = 18$

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

Subtract $6$ from both sides of the equation.

$- 3 x = 18 - 6$

Subtract $6$ from $18$ .

$- 3 x = 12$

Divide each term in $- 3 x = 12$ by $- 3$ and simplify.

Divide each term in $- 3 x = 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{12}{- 3}$

Divide $x$ by $1$ .

$x = \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$x = - 4$

Step 6

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

$(- 4, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 4, - 1)$

Equation Form:

$x = - 4, y = - 1$

Step 8

Solve by Addition/Elimination x+2y=-6 3x+8y=-20

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