Precalculus Examples

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

Step 1

Multiply each equation by the value that makes the coefficients of $x$ opposite.

$x + y = 4$

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

$x + y = 4$

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

Step 2.1.1.2

Rewrite $- 1 x$ as $- x$ .

$x + y = 4$

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

Step 2.1.1.3

Multiply $- 1 (- y)$ .

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Step 2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$x + y = 4$

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

Step 2.1.1.3.2

Multiply $y$ by $1$ .

$x + y = 4$

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

$x + y = 4$

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

$x + y = 4$

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

$x + y = 4$

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 1$ by $2$ .

$x + y = 4$

$- x + y = - 2$

$x + y = 4$

$- x + y = - 2$

$x + y = 4$

$- x + y = - 2$

Step 3

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

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

Step 4

Divide each term in $2 y = 2$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 y = 2$ by $2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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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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