Solve by Addition/Elimination 6x+3y=-12 6x+2y=-4

$6 x + 3 y = - 12$ $6 x + 2 y = - 4$

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

$(- 1) \cdot (6 x + 3 y) = (- 1) (- 12)$

$6 x + 2 y = - 4$

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (6 x + 3 y)$ .

Apply the distributive property.

$- 1 (6 x) - 1 (3 y) = (- 1) (- 12)$

$6 x + 2 y = - 4$

Multiply.

Multiply $6$ by $- 1$ .

$- 6 x - 1 (3 y) = (- 1) (- 12)$

$6 x + 2 y = - 4$

Multiply $3$ by $- 1$ .

$- 6 x - 3 y = (- 1) (- 12)$

$6 x + 2 y = - 4$

$- 6 x - 3 y = (- 1) (- 12)$

$6 x + 2 y = - 4$

$- 6 x - 3 y = (- 1) (- 12)$

$6 x + 2 y = - 4$

$- 6 x - 3 y = (- 1) (- 12)$

$6 x + 2 y = - 4$

Simplify the right side.

Multiply $- 1$ by $- 12$ .

$- 6 x - 3 y = 12$

$6 x + 2 y = - 4$

$- 6 x - 3 y = 12$

$6 x + 2 y = - 4$

$- 6 x - 3 y = 12$

$6 x + 2 y = - 4$

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

	$-$	$6$	$x$	$-$	$3$	$y$	$=$	$1$	$2$
$+$		$6$	$x$	$+$	$2$	$y$	$=$	$-$	$4$
					$-$	$y$	$=$		$8$

Divide each term in $- y = 8$ by $- 1$ and simplify.

Divide each term in $- y = 8$ by $- 1$ .

$\frac{- y}{- 1} = \frac{8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{8}{- 1}$

Divide $y$ by $1$ .

$y = \frac{8}{- 1}$

Simplify the right side.

Divide $8$ by $- 1$ .

$y = - 8$

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 $x$ .

$- 6 x - 3 \cdot - 8 = 12$

Multiply $- 3$ by $- 8$ .

$- 6 x + 24 = 12$

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

Subtract $24$ from both sides of the equation.

$- 6 x = 12 - 24$

Subtract $24$ from $12$ .

$- 6 x = - 12$

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

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

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 12$ by $- 6$ .

$x = 2$

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

$(2, - 8)$

The result can be shown in multiple forms.

Point Form:

$(2, - 8)$

Equation Form:

$x = 2, y = - 8$

Solve by Addition/Elimination 6x+3y=-12 6x+2y=-4

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