Algebra Examples

$2 x + y = 0$ , $- 2 x + 5 y = - 18$

Step 1

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

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

Step 2

Divide each term in $6 y = - 18$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 y = - 18$ by $6$ .

$\frac{6 y}{6} = \frac{- 18}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 18}{6}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 18}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 18$ by $6$ .

$y = - 3$

Step 3

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

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Step 3.1

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

$2 x - 3 = 0$

Step 3.2

Add $3$ to both sides of the equation.

$2 x = 3$

Step 3.3

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 4

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

$(\frac{3}{2}, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{3}{2}, - 3)$

Equation Form:

$x = \frac{3}{2}, y = - 3$

Step 6

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

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

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