Solve by Addition/Elimination 2x+4y=16 2x-4y=0

$2 x + 4 y = 16$ $2 x - 4 y = 0$

Step 1

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

$(- 1) \cdot (2 x + 4 y) = (- 1) (16)$

$2 x - 4 y = 0$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (2 x + 4 y)$ .

Apply the distributive property.

$- 1 (2 x) - 1 (4 y) = (- 1) (16)$

$2 x - 4 y = 0$

Multiply.

Multiply $2$ by $- 1$ .

$- 2 x - 1 (4 y) = (- 1) (16)$

$2 x - 4 y = 0$

Multiply $4$ by $- 1$ .

$- 2 x - 4 y = (- 1) (16)$

$2 x - 4 y = 0$

$- 2 x - 4 y = (- 1) (16)$

$2 x - 4 y = 0$

$- 2 x - 4 y = (- 1) (16)$

$2 x - 4 y = 0$

$- 2 x - 4 y = (- 1) (16)$

$2 x - 4 y = 0$

Simplify the right side.

Multiply $- 1$ by $16$ .

$- 2 x - 4 y = - 16$

$2 x - 4 y = 0$

$- 2 x - 4 y = - 16$

$2 x - 4 y = 0$

$- 2 x - 4 y = - 16$

$2 x - 4 y = 0$

Step 3

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

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

Step 4

Divide each term in $- 8 y = - 16$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 16$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 16}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 16}{- 8}$

Divide $y$ by $1$ .

$y = \frac{- 16}{- 8}$

Simplify the right side.

Divide $- 16$ by $- 8$ .

$y = 2$

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 $x$ .

$- 2 x - 4 \cdot 2 = - 16$

Multiply $- 4$ by $2$ .

$- 2 x - 8 = - 16$

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

Add $8$ to both sides of the equation.

$- 2 x = - 16 + 8$

Add $- 16$ and $8$ .

$- 2 x = - 8$

Divide each term in $- 2 x = - 8$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 8$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 8}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$x = 4$

Step 6

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

$(4, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, 2)$

Equation Form:

$x = 4, y = 2$

Step 8

Solve by Addition/Elimination 2x+4y=16 2x-4y=0

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