Solve by Addition/Elimination 2x-4y=5 -8x+16y=-15

$2 x - 4 y = 5$ $- 8 x + 16 y = - 15$

Step 1

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

$(4) \cdot (2 x - 4 y) = (4) (5)$

$- 8 x + 16 y = - 15$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$4 (2 x) + 4 (- 4 y) = (4) (5)$

$- 8 x + 16 y = - 15$

Multiply.

Multiply $2$ by $4$ .

$8 x + 4 (- 4 y) = (4) (5)$

$- 8 x + 16 y = - 15$

Multiply $- 4$ by $4$ .

$8 x - 16 y = (4) (5)$

$- 8 x + 16 y = - 15$

$8 x - 16 y = (4) (5)$

$- 8 x + 16 y = - 15$

$8 x - 16 y = (4) (5)$

$- 8 x + 16 y = - 15$

$8 x - 16 y = (4) (5)$

$- 8 x + 16 y = - 15$

Simplify the right side.

Multiply $4$ by $5$ .

$8 x - 16 y = 20$

$- 8 x + 16 y = - 15$

$8 x - 16 y = 20$

$- 8 x + 16 y = - 15$

$8 x - 16 y = 20$

$- 8 x + 16 y = - 15$

Step 3

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

				$8$	$x$	$-$	$1$	$6$	$y$	$=$		$2$	$0$
$+$			$-$	$8$	$x$	$+$	$1$	$6$	$y$	$=$	$-$	$1$	$5$
									$0$	$=$			$5$

Step 4

Since $0 \neq 5$ , there are no solutions.

No solution

Step 5

Related Questions