Examples

x + y = 4

$x + y = 4$ ,

x - y = 2

$x - y = 2$

Step 1

Multiply each equation by the value that makes the coefficients of

x

$x$ opposite.

x + y = 4

$x + y = 4$

(- 1) \cdot (x - y) = (- 1) (2)

$(- 1) \cdot (x - y) = (- 1) (2)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify

(- 1) \cdot (x - y)

$(- 1) \cdot (x - y)$ .

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Step 2.1.1.1

Apply the distributive property.

x + y = 4

$x + y = 4$

- 1 x - 1 (- y) = (- 1) (2)

$- 1 x - 1 (- y) = (- 1) (2)$

Step 2.1.1.2

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

x + y = 4

$x + y = 4$

- x - 1 (- y) = (- 1) (2)

$- x - 1 (- y) = (- 1) (2)$

Step 2.1.1.3

Multiply

- 1 (- y)

$- 1 (- y)$ .

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Step 2.1.1.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

x + y = 4

$x + y = 4$

- x + 1 y = (- 1) (2)

$- x + 1 y = (- 1) (2)$

Step 2.1.1.3.2

Multiply

y

$y$ by

1

$1$ .

x + y = 4

$x + y = 4$

- x + y = (- 1) (2)

$- x + y = (- 1) (2)$

x + y = 4

$x + y = 4$

- x + y = (- 1) (2)

$- x + y = (- 1) (2)$

x + y = 4

$x + y = 4$

- x + y = (- 1) (2)

$- x + y = (- 1) (2)$

x + y = 4

$x + y = 4$

- x + y = (- 1) (2)

$- x + y = (- 1) (2)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply

- 1

$- 1$ by

2

$2$ .

x + y = 4

$x + y = 4$

- x + y = - 2

$- x + y = - 2$

x + y = 4

$x + y = 4$

- x + y = - 2

$- x + y = - 2$

x + y = 4

$x + y = 4$

- x + y = - 2

$- x + y = - 2$

Step 3

Add the two equations together to eliminate

x

$x$ from the system.

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

Step 4

Divide each term in

2 y = 2

$2 y = 2$ by

2

$2$ and simplify.

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Step 4.1

Divide each term in

2 y = 2

$2 y = 2$ by

2

$2$ .

\frac{2 y}{2} = \frac{2}{2}

$\frac{2 y}{2} = \frac{2}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

2

$2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{2}{2}$

Step 4.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{2}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide

$2$ by

$2$ .

$y = 1$

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

$x$ .

$x + 1 = 4$

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

$1$ from both sides of the equation.

$x = 4 - 1$

Step 5.2.2

Subtract

$1$ from

$4$ .

$x = 3$

Step 6

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

$(3, 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

Step 8

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