Algebra Examples

$y = 6 x + 9$ , $y = 12 + 6 x$

Step 1

Solve the system of equations.

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Step 1.1

Simplify the right side.

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Step 1.1.1

Reorder $12$ and $6 x$ .

$y = 6 x + 12$

$y = 6 x + 9$

$y = 6 x + 12$

$y = 6 x + 9$

Step 1.2

Move all terms containing variables to the left.

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Step 1.2.1

Subtract $6 x$ from both sides of the equation.

$y - 6 x = 9, y = 6 x + 12$

Step 1.2.2

Subtract $6 x$ from both sides of the equation.

$y - 6 x = 9, y - 6 x = 12$

Step 1.3

Reorder the polynomial.

$- 6 x + y = 9$

$y - 6 x = 12$

Step 1.4

Reorder the polynomial.

$- 6 x + y = 12$

$- 6 x + y = 9$

Step 1.5

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

$- 6 x + y = 9$

$(- 1) \cdot (- 6 x + y) = (- 1) (12)$

Step 1.6

Simplify.

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Step 1.6.1

Simplify the left side.

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Step 1.6.1.1

Simplify $(- 1) \cdot (- 6 x + y)$ .

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Step 1.6.1.1.1

Apply the distributive property.

$- 6 x + y = 9$

$- 1 (- 6 x) - 1 y = (- 1) (12)$

Step 1.6.1.1.2

Simplify the expression.

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Step 1.6.1.1.2.1

Multiply $- 6$ by $- 1$ .

$- 6 x + y = 9$

$6 x - 1 y = (- 1) (12)$

Step 1.6.1.1.2.2

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

$- 6 x + y = 9$

$6 x - y = (- 1) (12)$

$- 6 x + y = 9$

$6 x - y = (- 1) (12)$

$- 6 x + y = 9$

$6 x - y = (- 1) (12)$

$- 6 x + y = 9$

$6 x - y = (- 1) (12)$

Step 1.6.2

Simplify the right side.

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Step 1.6.2.1

Multiply $- 1$ by $12$ .

$- 6 x + y = 9$

$6 x - y = - 12$

$- 6 x + y = 9$

$6 x - y = - 12$

$- 6 x + y = 9$

$6 x - y = - 12$

Step 1.7

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

	$-$	$6$	$x$	$+$	$y$	$=$			$9$
$+$		$6$	$x$	$-$	$y$	$=$	$-$	$1$	$2$
					$0$	$=$		$-$	$3$

Step 1.8

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

	$-$	$6$	$x$	$+$	$y$	$=$			$9$
$+$		$6$	$x$	$-$	$y$	$=$	$-$	$1$	$2$
					$0$	$=$		$-$	$3$

	$-$	$6$	$x$	$+$	$y$	$=$			$9$
$+$		$6$	$x$	$-$	$y$	$=$	$-$	$1$	$2$
					$0$	$=$		$-$	$3$

	$-$	$6$	$x$	$+$	$y$	$=$			$9$
$+$		$6$	$x$	$-$	$y$	$=$	$-$	$1$	$2$
					$0$	$=$		$-$	$3$