Examples

$x + y = 3$ , $x + y = 6$

Step 1

Solve the system of equations.

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Step 1.1

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

$x + y = 3$

$(- 1) \cdot (x + y) = (- 1) (6)$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Simplify $(- 1) \cdot (x + y)$ .

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Step 1.2.1.1.1

Apply the distributive property.

$x + y = 3$

$- 1 x - 1 y = (- 1) (6)$

Step 1.2.1.1.2

Rewrite negatives.

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Step 1.2.1.1.2.1

Rewrite $- 1 x$ as $- x$ .

$x + y = 3$

$- x - 1 y = (- 1) (6)$

Step 1.2.1.1.2.2

Rewrite $- 1 y$ as $- y$ .

$x + y = 3$

$- x - y = (- 1) (6)$

$x + y = 3$

$- x - y = (- 1) (6)$

$x + y = 3$

$- x - y = (- 1) (6)$

$x + y = 3$

$- x - y = (- 1) (6)$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Multiply $- 1$ by $6$ .

$x + y = 3$

$- x - y = - 6$

$x + y = 3$

$- x - y = - 6$

$x + y = 3$

$- x - y = - 6$

Step 1.3

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

		$x$	$+$	$y$	$=$		$3$
$+$	$-$	$x$	$-$	$y$	$=$	$-$	$6$
				$0$	$=$	$-$	$3$

Step 1.4

Since $0 \neq - 3$ , there are no solutions.

No solution

Step 2

Since the system has no solution, the equations and graphs are parallel and do not intersect. Thus, the system is inconsistent.

Inconsistent

Step 3

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