Precalculus Examples

$4 x + 6 y = 0$ $x - 2 y = 14$

Step 1

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

$4 x + 6 y = 0$

$(- 4) \cdot (x - 2 y) = (- 4) (14)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(- 4) \cdot (x - 2 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$4 x + 6 y = 0$

$- 4 x - 4 (- 2 y) = (- 4) (14)$

Step 2.1.1.2

Multiply $- 2$ by $- 4$ .

$4 x + 6 y = 0$

$- 4 x + 8 y = (- 4) (14)$

$4 x + 6 y = 0$

$- 4 x + 8 y = (- 4) (14)$

$4 x + 6 y = 0$

$- 4 x + 8 y = (- 4) (14)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 4$ by $14$ .

$4 x + 6 y = 0$

$- 4 x + 8 y = - 56$

$4 x + 6 y = 0$

$- 4 x + 8 y = - 56$

$4 x + 6 y = 0$

$- 4 x + 8 y = - 56$

Step 3

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

		$4$	$x$	$+$	$6$	$y$	$=$			$0$
$+$	$-$	$4$	$x$	$+$	$8$	$y$	$=$	$-$	$5$	$6$
				$1$	$4$	$y$	$=$	$-$	$5$	$6$

Step 4

Divide each term in $14 y = - 56$ by $14$ and simplify.

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Step 4.1

Divide each term in $14 y = - 56$ by $14$ .

$\frac{14 y}{14} = \frac{- 56}{14}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $14$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{14 y}{14} = \frac{- 56}{14}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 56}{14}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 56$ by $14$ .

$y = - 4$

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 $x$ .

$4 x + 6 (- 4) = 0$

Step 5.2

Multiply $6$ by $- 4$ .

$4 x - 24 = 0$

Step 5.3

Add $24$ to both sides of the equation.

$4 x = 24$

Step 5.4

Divide each term in $4 x = 24$ by $4$ and simplify.

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Step 5.4.1

Divide each term in $4 x = 24$ by $4$ .

$\frac{4 x}{4} = \frac{24}{4}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $4$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{24}{4}$

Step 5.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{4}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $24$ by $4$ .

$x = 6$

Step 6

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

$(6, - 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(6, - 4)$

Equation Form:

$x = 6, y = - 4$

Step 8

		$4$	$x$	$+$	$6$	$y$	$=$			$0$
$+$	$-$	$4$	$x$	$+$	$8$	$y$	$=$	$-$	$5$	$6$
				$1$	$4$	$y$	$=$	$-$	$5$	$6$

		$4$	$x$	$+$	$6$	$y$	$=$			$0$
$+$	$-$	$4$	$x$	$+$	$8$	$y$	$=$	$-$	$5$	$6$
				$1$	$4$	$y$	$=$	$-$	$5$	$6$

		$4$	$x$	$+$	$6$	$y$	$=$			$0$
$+$	$-$	$4$	$x$	$+$	$8$	$y$	$=$	$-$	$5$	$6$
				$1$	$4$	$y$	$=$	$-$	$5$	$6$