Solve by Addition/Elimination 3x-5y=17 9x-15y=-4

$3 x - 5 y = 17$ $9 x - 15 y = - 4$

Step 1

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

$(- 3) \cdot (3 x - 5 y) = (- 3) (17)$

$9 x - 15 y = - 4$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (3 x - 5 y)$ .

Apply the distributive property.

$- 3 (3 x) - 3 (- 5 y) = (- 3) (17)$

$9 x - 15 y = - 4$

Multiply.

Multiply $3$ by $- 3$ .

$- 9 x - 3 (- 5 y) = (- 3) (17)$

$9 x - 15 y = - 4$

Multiply $- 5$ by $- 3$ .

$- 9 x + 15 y = (- 3) (17)$

$9 x - 15 y = - 4$

$- 9 x + 15 y = (- 3) (17)$

$9 x - 15 y = - 4$

$- 9 x + 15 y = (- 3) (17)$

$9 x - 15 y = - 4$

$- 9 x + 15 y = (- 3) (17)$

$9 x - 15 y = - 4$

Simplify the right side.

Multiply $- 3$ by $17$ .

$- 9 x + 15 y = - 51$

$9 x - 15 y = - 4$

$- 9 x + 15 y = - 51$

$9 x - 15 y = - 4$

$- 9 x + 15 y = - 51$

$9 x - 15 y = - 4$

Step 3

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

			$-$	$9$	$x$	$+$	$1$	$5$	$y$	$=$	$-$	$5$	$1$
$+$				$9$	$x$	$-$	$1$	$5$	$y$	$=$		$-$	$4$
									$0$	$=$	$-$	$5$	$5$

Step 4

Since $0 \neq - 55$ , there are no solutions.

No solution

Step 5

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