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

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

Step 1

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

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

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

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

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

Multiply.

Multiply $2$ by $- 3$ .

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

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

Multiply $- 4$ by $- 3$ .

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

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

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

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

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

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

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

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

Simplify the right side.

Multiply $- 3$ by $8$ .

$- 6 x + 12 y = - 24$

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

$- 6 x + 12 y = - 24$

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

Simplify the left side.

Simplify $(2) \cdot (3 x + 8 y)$ .

Apply the distributive property.

$- 6 x + 12 y = - 24$

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

Multiply.

Multiply $3$ by $2$ .

$- 6 x + 12 y = - 24$

$6 x + 2 (8 y) = (2) (- 2)$

Multiply $8$ by $2$ .

$- 6 x + 12 y = - 24$

$6 x + 16 y = (2) (- 2)$

$- 6 x + 12 y = - 24$

$6 x + 16 y = (2) (- 2)$

$- 6 x + 12 y = - 24$

$6 x + 16 y = (2) (- 2)$

$- 6 x + 12 y = - 24$

$6 x + 16 y = (2) (- 2)$

Simplify the right side.

Multiply $2$ by $- 2$ .

$- 6 x + 12 y = - 24$

$6 x + 16 y = - 4$

$- 6 x + 12 y = - 24$

$6 x + 16 y = - 4$

$- 6 x + 12 y = - 24$

$6 x + 16 y = - 4$

Step 3

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

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

Step 4

Divide each term in $28 y = - 28$ by $28$ and simplify.

Divide each term in $28 y = - 28$ by $28$ .

$\frac{28 y}{28} = \frac{- 28}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 y}{28} = \frac{- 28}{28}$

Divide $y$ by $1$ .

$y = \frac{- 28}{28}$

Simplify the right side.

Divide $- 28$ by $28$ .

$y = - 1$

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 $x$ .

$- 6 x + 12 (- 1) = - 24$

Multiply $12$ by $- 1$ .

$- 6 x - 12 = - 24$

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

Add $12$ to both sides of the equation.

$- 6 x = - 24 + 12$

Add $- 24$ and $12$ .

$- 6 x = - 12$

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 $- 6$ .

$x = 2$

Step 6

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

$(2, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 1)$

Equation Form:

$x = 2, y = - 1$

Step 8

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

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