Precalculus Examples

$x + 2 y = 4$ , $2 x + 4 y = 8$

Step 1

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

$(- 2) \cdot (x + 2 y) = (- 2) (4)$

$2 x + 4 y = 8$

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.

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

$2 x + 4 y = 8$

Step 2.1.1.2

Multiply $2$ by $- 2$ .

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

$2 x + 4 y = 8$

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

$2 x + 4 y = 8$

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

$2 x + 4 y = 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 2$ by $4$ .

$- 2 x - 4 y = - 8$

$2 x + 4 y = 8$

$- 2 x - 4 y = - 8$

$2 x + 4 y = 8$

$- 2 x - 4 y = - 8$

$2 x + 4 y = 8$

Step 3

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

	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$8$
$+$		$2$	$x$	$+$	$4$	$y$	$=$		$8$
						$0$	$=$		$0$

Step 4

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Step 5

Solve one of the equations for $y$ .

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Step 5.1

Add $2 x$ to both sides of the equation.

$- 4 y = - 8 + 2 x$

Step 5.2

Divide each term in $- 4 y = - 8 + 2 x$ by $- 4$ and simplify.

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Step 5.2.1

Divide each term in $- 4 y = - 8 + 2 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 8}{- 4} + \frac{2 x}{- 4}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 4$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 8}{- 4} + \frac{2 x}{- 4}$

Step 5.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 8}{- 4} + \frac{2 x}{- 4}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Simplify each term.

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Step 5.2.3.1.1

Divide $- 8$ by $- 4$ .

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

Step 5.2.3.1.2

Cancel the common factor of $2$ and $- 4$ .

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Step 5.2.3.1.2.1

Factor $2$ out of $2 x$ .

$y = 2 + \frac{2 (x)}{- 4}$

Step 5.2.3.1.2.2

Cancel the common factors.

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Step 5.2.3.1.2.2.1

Factor $2$ out of $- 4$ .

$y = 2 + \frac{2 x}{2 \cdot - 2}$

Step 5.2.3.1.2.2.2

Cancel the common factor.

$y = 2 + \frac{2 x}{2 \cdot - 2}$

Step 5.2.3.1.2.2.3

Rewrite the expression.

$y = 2 + \frac{x}{- 2}$

Step 5.2.3.1.3

Move the negative in front of the fraction.

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

Step 6

The solution is the set of ordered pairs that make $y = 2 - \frac{x}{2}$ true.

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

Step 7

The result can be shown in multiple forms.

Point Form:

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

Equation Form:

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

Step 8

Enter YOUR Problem

	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$8$
$+$		$2$	$x$	$+$	$4$	$y$	$=$		$8$
						$0$	$=$		$0$

	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$8$
$+$		$2$	$x$	$+$	$4$	$y$	$=$		$8$
						$0$	$=$		$0$

	$-$	$2$	$x$	$-$	$4$	$y$	$=$	$-$	$8$
$+$		$2$	$x$	$+$	$4$	$y$	$=$		$8$
						$0$	$=$		$0$