Solve by Addition/Elimination 2x+4y=8 3x-3y=12

$2 x + 4 y = 8$ $3 x - 3 y = 12$

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

$(- 3) \cdot (2 x + 4 y) = (- 3) (8)$

$(2) \cdot (3 x - 3 y) = (2) (12)$

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (2 x + 4 y)$ .

Apply the distributive property.

$- 3 (2 x) - 3 (4 y) = (- 3) (8)$

$(2) \cdot (3 x - 3 y) = (2) (12)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 (4 y) = (- 3) (8)$

$(2) \cdot (3 x - 3 y) = (2) (12)$

Multiply $4$ by $- 3$ .

$- 6 x - 12 y = (- 3) (8)$

$(2) \cdot (3 x - 3 y) = (2) (12)$

$- 6 x - 12 y = (- 3) (8)$

$(2) \cdot (3 x - 3 y) = (2) (12)$

$- 6 x - 12 y = (- 3) (8)$

$(2) \cdot (3 x - 3 y) = (2) (12)$

$- 6 x - 12 y = (- 3) (8)$

$(2) \cdot (3 x - 3 y) = (2) (12)$

Simplify the right side.

Multiply $- 3$ by $8$ .

$- 6 x - 12 y = - 24$

$(2) \cdot (3 x - 3 y) = (2) (12)$

$- 6 x - 12 y = - 24$

$(2) \cdot (3 x - 3 y) = (2) (12)$

Simplify the left side.

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

Apply the distributive property.

$- 6 x - 12 y = - 24$

$2 (3 x) + 2 (- 3 y) = (2) (12)$

Multiply.

Multiply $3$ by $2$ .

$- 6 x - 12 y = - 24$

$6 x + 2 (- 3 y) = (2) (12)$

Multiply $- 3$ by $2$ .

$- 6 x - 12 y = - 24$

$6 x - 6 y = (2) (12)$

$- 6 x - 12 y = - 24$

$6 x - 6 y = (2) (12)$

$- 6 x - 12 y = - 24$

$6 x - 6 y = (2) (12)$

$- 6 x - 12 y = - 24$

$6 x - 6 y = (2) (12)$

Simplify the right side.

Multiply $2$ by $12$ .

$- 6 x - 12 y = - 24$

$6 x - 6 y = 24$

$- 6 x - 12 y = - 24$

$6 x - 6 y = 24$

$- 6 x - 12 y = - 24$

$6 x - 6 y = 24$

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

	$-$	$6$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$2$	$4$
$+$		$6$	$x$		$-$	$6$	$y$	$=$		$2$	$4$
				$-$	$1$	$8$	$y$	$=$			$0$

Divide each term in $- 18 y = 0$ by $- 18$ and simplify.

Divide each term in $- 18 y = 0$ by $- 18$ .

$\frac{- 18 y}{- 18} = \frac{0}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 y}{- 18} = \frac{0}{- 18}$

Divide $y$ by $1$ .

$y = \frac{0}{- 18}$

Simplify the right side.

Divide $0$ by $- 18$ .

$y = 0$

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 $x$ .

$- 6 x - 12 \cdot 0 = - 24$

Simplify $- 6 x - 12 \cdot 0$ .

Multiply $- 12$ by $0$ .

$- 6 x + 0 = - 24$

Add $- 6 x$ and $0$ .

$- 6 x = - 24$

Divide each term in $- 6 x = - 24$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 24$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 24}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 24}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 6}$

Simplify the right side.

Divide $- 24$ by $- 6$ .

$x = 4$

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

$(4, 0)$

The result can be shown in multiple forms.

Point Form:

$(4, 0)$

Equation Form:

$x = 4, y = 0$

Solve by Addition/Elimination 2x+4y=8 3x-3y=12

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