Precalculus Examples

$7 x - 6 y = - 5$ , $- 42 x + 36 y = 31$

Step 1

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

$(6) \cdot (7 x - 6 y) = (6) (- 5)$

$- 42 x + 36 y = 31$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(6) \cdot (7 x - 6 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$6 (7 x) + 6 (- 6 y) = (6) (- 5)$

$- 42 x + 36 y = 31$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $7$ by $6$ .

$42 x + 6 (- 6 y) = (6) (- 5)$

$- 42 x + 36 y = 31$

Step 2.1.1.2.2

Multiply $- 6$ by $6$ .

$42 x - 36 y = (6) (- 5)$

$- 42 x + 36 y = 31$

$42 x - 36 y = (6) (- 5)$

$- 42 x + 36 y = 31$

$42 x - 36 y = (6) (- 5)$

$- 42 x + 36 y = 31$

$42 x - 36 y = (6) (- 5)$

$- 42 x + 36 y = 31$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $6$ by $- 5$ .

$42 x - 36 y = - 30$

$- 42 x + 36 y = 31$

$42 x - 36 y = - 30$

$- 42 x + 36 y = 31$

$42 x - 36 y = - 30$

$- 42 x + 36 y = 31$

Step 3

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

		$4$	$2$	$x$	$-$	$3$	$6$	$y$	$=$	$-$	$3$	$0$
$+$	$-$	$4$	$2$	$x$	$+$	$3$	$6$	$y$	$=$		$3$	$1$
								$0$	$=$			$1$

Step 4

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

No solution

Step 5

		$4$	$2$	$x$	$-$	$3$	$6$	$y$	$=$	$-$	$3$	$0$
$+$	$-$	$4$	$2$	$x$	$+$	$3$	$6$	$y$	$=$		$3$	$1$
								$0$	$=$			$1$

		$4$	$2$	$x$	$-$	$3$	$6$	$y$	$=$	$-$	$3$	$0$
$+$	$-$	$4$	$2$	$x$	$+$	$3$	$6$	$y$	$=$		$3$	$1$
								$0$	$=$			$1$

		$4$	$2$	$x$	$-$	$3$	$6$	$y$	$=$	$-$	$3$	$0$
$+$	$-$	$4$	$2$	$x$	$+$	$3$	$6$	$y$	$=$		$3$	$1$
								$0$	$=$			$1$