Examples

$2 x + y = - 2$ ,

$x + 2 y = 2$

Step 1

Multiply each equation by the value that makes the coefficients of

$x$ opposite.

$2 x + y = - 2$

$(- 2) \cdot (x + 2 y) = (- 2) (2)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify

$(- 2) \cdot (x + 2 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$2 x + y = - 2$

$- 2 x - 2 (2 y) = (- 2) (2)$

Step 2.1.1.2

Multiply

$2$ by

$- 2$ .

$2 x + y = - 2$

$- 2 x - 4 y = (- 2) (2)$

$2 x + y = - 2$

$- 2 x - 4 y = (- 2) (2)$

$2 x + y = - 2$

$- 2 x - 4 y = (- 2) (2)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply

$- 2$ by

$2$ .

$2 x + y = - 2$

$- 2 x - 4 y = - 4$

$2 x + y = - 2$

$- 2 x - 4 y = - 4$

$2 x + y = - 2$

$- 2 x - 4 y = - 4$

Step 3

Add the two equations together to eliminate

$x$ from the system.

		$2$	$x$	$+$		$y$	$=$	$-$	$2$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$4$
				$-$	$3$	$y$	$=$	$-$	$6$

Step 4

Divide each term in

$- 3 y = - 6$ by

$- 3$ and simplify.

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Step 4.1

Divide each term in

$- 3 y = - 6$ by

$- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

$- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Step 4.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{- 6}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide

$- 6$ by

$- 3$ .

$y = 2$

Step 5

Substitute the value found for

$y$ into one of the original equations, then solve for

$x$ .

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Step 5.1

Substitute the value found for

$y$ into one of the original equations to solve for

$x$ .

$2 x + 2 = - 2$

Step 5.2

Move all terms not containing

$x$ to the right side of the equation.

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Step 5.2.1

Subtract

$2$ from both sides of the equation.

$2 x = - 2 - 2$

Step 5.2.2

Subtract

$2$ from

$- 2$ .

$2 x = - 4$

Step 5.3

Divide each term in

$2 x = - 4$ by

$2$ and simplify.

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Step 5.3.1

Divide each term in

$2 x = - 4$ by

$2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of

$2$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Step 5.3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{- 4}{2}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide

$- 4$ by

$2$ .

$x = - 2$

Step 6

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

$(- 2, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 2, 2)$

Equation Form:

$x = - 2, y = 2$

Step 8

Enter YOUR Problem

		$2$	$x$	$+$		$y$	$=$	$-$	$2$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$4$
				$-$	$3$	$y$	$=$	$-$	$6$

		$2$	$x$	$+$		$y$	$=$	$-$	$2$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$4$
				$-$	$3$	$y$	$=$	$-$	$6$

		$2$	$x$	$+$		$y$	$=$	$-$	$2$
$+$	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$4$
				$-$	$3$	$y$	$=$	$-$	$6$