Algebra Examples

$2 x - y = - 22$ $y = 7 x + 67$

Step 1

Subtract $7 x$ from both sides of the equation.

$2 x - y = - 22, y - 7 x = 67$

Step 2

Reorder the polynomial.

$- 7 x + y = 67$

$2 x - y = - 22$

Step 3

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

		$2$	$x$	$-$	$y$	$=$	$-$	$2$	$2$
$+$	$-$	$7$	$x$	$+$	$y$	$=$		$6$	$7$
	$-$	$5$	$x$			$=$		$4$	$5$

Step 4

Divide each term in $- 5 x = 45$ by $- 5$ and simplify.

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Step 4.1

Divide each term in $- 5 x = 45$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{45}{- 5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{45}{- 5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{45}{- 5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $45$ by $- 5$ .

$x = - 9$

Step 5

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

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Step 5.1

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$2 (- 9) - y = - 22$

Step 5.2

Multiply $2$ by $- 9$ .

$- 18 - y = - 22$

Step 5.3

Move all terms not containing $y$ to the right side of the equation.

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Step 5.3.1

Add $18$ to both sides of the equation.

$- y = - 22 + 18$

Step 5.3.2

Add $- 22$ and $18$ .

$- y = - 4$

Step 5.4

Divide each term in $- y = - 4$ by $- 1$ and simplify.

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Step 5.4.1

Divide each term in $- y = - 4$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 4}{- 1}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 4}{- 1}$

Step 5.4.2.2

Divide $y$ by $1$ .

$y = \frac{- 4}{- 1}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $- 4$ by $- 1$ .

$y = 4$

Step 6

The solution to the independent system of equations can be represented as a point.

$(- 9, 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 9, 4)$

Equation Form:

$x = - 9, y = 4$

Step 8

		$2$	$x$	$-$	$y$	$=$	$-$	$2$	$2$
$+$	$-$	$7$	$x$	$+$	$y$	$=$		$6$	$7$
	$-$	$5$	$x$			$=$		$4$	$5$

		$2$	$x$	$-$	$y$	$=$	$-$	$2$	$2$
$+$	$-$	$7$	$x$	$+$	$y$	$=$		$6$	$7$
	$-$	$5$	$x$			$=$		$4$	$5$

		$2$	$x$	$-$	$y$	$=$	$-$	$2$	$2$
$+$	$-$	$7$	$x$	$+$	$y$	$=$		$6$	$7$
	$-$	$5$	$x$			$=$		$4$	$5$