Solve by Addition/Elimination -4x-2y=-12 and 4x+8y=-24

$- 4 x - 2 y = - 12$ and $4 x + 8 y = - 24$

Step 1

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

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

Step 2

Divide each term in $6 y = - 36$ by $6$ and simplify.

Divide each term in $6 y = - 36$ by $6$ .

$\frac{6 y}{6} = \frac{- 36}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 36}{6}$

Divide $y$ by $1$ .

$y = \frac{- 36}{6}$

Simplify the right side.

Divide $- 36$ by $6$ .

$y = - 6$

Step 3

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 $x$ .

$- 4 x - 2 \cdot - 6 = - 12$

Multiply $- 2$ by $- 6$ .

$- 4 x + 12 = - 12$

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

Subtract $12$ from both sides of the equation.

$- 4 x = - 12 - 12$

Subtract $12$ from $- 12$ .

$- 4 x = - 24$

Divide each term in $- 4 x = - 24$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 24$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 24}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 24}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 4}$

Simplify the right side.

Divide $- 24$ by $- 4$ .

$x = 6$

Step 4

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

$(6, - 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(6, - 6)$

Equation Form:

$x = 6, y = - 6$

Step 6

Solve by Addition/Elimination -4x-2y=-12 and 4x+8y=-24

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