Algebra Examples

$- 5 x + 8 y = 0$ $- 7 x - 8 y = - 96$

Step 1

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

		$-$	$5$	$x$	$+$	$8$	$y$	$=$			$0$
$+$		$-$	$7$	$x$	$-$	$8$	$y$	$=$	$-$	$9$	$6$
	$-$	$1$	$2$	$x$				$=$	$-$	$9$	$6$

Step 2

Divide each term in $- 12 x = - 96$ by $- 12$ and simplify.

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Step 2.1

Divide each term in $- 12 x = - 96$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 96}{- 12}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 12$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 96}{- 12}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 96}{- 12}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 96$ by $- 12$ .

$x = 8$

Step 3

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

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Step 3.1

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

$- 5 \cdot 8 + 8 y = 0$

Step 3.2

Multiply $- 5$ by $8$ .

$- 40 + 8 y = 0$

Step 3.3

Add $40$ to both sides of the equation.

$8 y = 40$

Step 3.4

Divide each term in $8 y = 40$ by $8$ and simplify.

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Step 3.4.1

Divide each term in $8 y = 40$ by $8$ .

$\frac{8 y}{8} = \frac{40}{8}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $8$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{40}{8}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{40}{8}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $40$ by $8$ .

$y = 5$

Step 4

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

$(8, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(8, 5)$

Equation Form:

$x = 8, y = 5$

Step 6

		$-$	$5$	$x$	$+$	$8$	$y$	$=$			$0$
$+$		$-$	$7$	$x$	$-$	$8$	$y$	$=$	$-$	$9$	$6$
	$-$	$1$	$2$	$x$				$=$	$-$	$9$	$6$

		$-$	$5$	$x$	$+$	$8$	$y$	$=$			$0$
$+$		$-$	$7$	$x$	$-$	$8$	$y$	$=$	$-$	$9$	$6$
	$-$	$1$	$2$	$x$				$=$	$-$	$9$	$6$

		$-$	$5$	$x$	$+$	$8$	$y$	$=$			$0$
$+$		$-$	$7$	$x$	$-$	$8$	$y$	$=$	$-$	$9$	$6$
	$-$	$1$	$2$	$x$				$=$	$-$	$9$	$6$