Solve by Addition/Elimination 4x-5y=0 8x-10y=15

$4 x - 5 y = 0$ $8 x - 10 y = 15$

Step 1

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

$(- 2) \cdot (4 x - 5 y) = (- 2) (0)$

$8 x - 10 y = 15$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (4 x - 5 y)$ .

Apply the distributive property.

$- 2 (4 x) - 2 (- 5 y) = (- 2) (0)$

$8 x - 10 y = 15$

Multiply.

Multiply $4$ by $- 2$ .

$- 8 x - 2 (- 5 y) = (- 2) (0)$

$8 x - 10 y = 15$

Multiply $- 5$ by $- 2$ .

$- 8 x + 10 y = (- 2) (0)$

$8 x - 10 y = 15$

$- 8 x + 10 y = (- 2) (0)$

$8 x - 10 y = 15$

$- 8 x + 10 y = (- 2) (0)$

$8 x - 10 y = 15$

$- 8 x + 10 y = (- 2) (0)$

$8 x - 10 y = 15$

Simplify the right side.

Multiply $- 2$ by $0$ .

$- 8 x + 10 y = 0$

$8 x - 10 y = 15$

$- 8 x + 10 y = 0$

$8 x - 10 y = 15$

$- 8 x + 10 y = 0$

$8 x - 10 y = 15$

Step 3

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

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

Step 4

Since $0 \neq 15$ , there are no solutions.

No solution

Step 5

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