Precalculus Examples

$2 x - y = 3$ , $4 x - 2 y = 5$

Step 1

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

$(- 2) \cdot (2 x - y) = (- 2) (3)$

$4 x - 2 y = 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

$- 2 (2 x) - 2 (- y) = (- 2) (3)$

$4 x - 2 y = 5$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $2$ by $- 2$ .

$- 4 x - 2 (- y) = (- 2) (3)$

$4 x - 2 y = 5$

Step 2.1.1.2.2

Multiply $- 1$ by $- 2$ .

$- 4 x + 2 y = (- 2) (3)$

$4 x - 2 y = 5$

$- 4 x + 2 y = (- 2) (3)$

$4 x - 2 y = 5$

$- 4 x + 2 y = (- 2) (3)$

$4 x - 2 y = 5$

$- 4 x + 2 y = (- 2) (3)$

$4 x - 2 y = 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 2$ by $3$ .

$- 4 x + 2 y = - 6$

$4 x - 2 y = 5$

$- 4 x + 2 y = - 6$

$4 x - 2 y = 5$

$- 4 x + 2 y = - 6$

$4 x - 2 y = 5$

Step 3

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

	$-$	$4$	$x$	$+$	$2$	$y$	$=$	$-$	$6$
$+$		$4$	$x$	$-$	$2$	$y$	$=$		$5$
						$0$	$=$	$-$	$1$

Step 4

Since $0 \neq - 1$ , there are no solutions.

No solution

Step 5

	$-$	$4$	$x$	$+$	$2$	$y$	$=$	$-$	$6$
$+$		$4$	$x$	$-$	$2$	$y$	$=$		$5$
						$0$	$=$	$-$	$1$

	$-$	$4$	$x$	$+$	$2$	$y$	$=$	$-$	$6$
$+$		$4$	$x$	$-$	$2$	$y$	$=$		$5$
						$0$	$=$	$-$	$1$

	$-$	$4$	$x$	$+$	$2$	$y$	$=$	$-$	$6$
$+$		$4$	$x$	$-$	$2$	$y$	$=$		$5$
						$0$	$=$	$-$	$1$