Precalculus Examples

$2 x - 4 y = 4$ , $10 x - 20 y = 8$

Step 1

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

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

$10 x - 20 y = 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

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

$10 x - 20 y = 8$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $2$ by $- 5$ .

$- 10 x - 5 (- 4 y) = (- 5) (4)$

$10 x - 20 y = 8$

Step 2.1.1.2.2

Multiply $- 4$ by $- 5$ .

$- 10 x + 20 y = (- 5) (4)$

$10 x - 20 y = 8$

$- 10 x + 20 y = (- 5) (4)$

$10 x - 20 y = 8$

$- 10 x + 20 y = (- 5) (4)$

$10 x - 20 y = 8$

$- 10 x + 20 y = (- 5) (4)$

$10 x - 20 y = 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 5$ by $4$ .

$- 10 x + 20 y = - 20$

$10 x - 20 y = 8$

$- 10 x + 20 y = - 20$

$10 x - 20 y = 8$

$- 10 x + 20 y = - 20$

$10 x - 20 y = 8$

Step 3

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

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

Step 4

Since $0 \neq - 12$ , there are no solutions.

No solution

Step 5

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

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

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