Precalculus Examples

$x + 4 y = 6$ , $x = 8 y$

Step 1

Subtract $8 y$ from both sides of the equation.

$x + 4 y = 6, x - 8 y = 0$

Step 2

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

$x + 4 y = 6$

$(- 1) \cdot (x - 8 y) = (- 1) (0)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $(- 1) \cdot (x - 8 y)$ .

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Step 3.1.1.1

Apply the distributive property.

$x + 4 y = 6$

$- 1 x - 1 (- 8 y) = (- 1) (0)$

Step 3.1.1.2

Simplify the expression.

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Step 3.1.1.2.1

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

$x + 4 y = 6$

$- x - 1 (- 8 y) = (- 1) (0)$

Step 3.1.1.2.2

Multiply $- 8$ by $- 1$ .

$x + 4 y = 6$

$- x + 8 y = (- 1) (0)$

$x + 4 y = 6$

$- x + 8 y = (- 1) (0)$

$x + 4 y = 6$

$- x + 8 y = (- 1) (0)$

$x + 4 y = 6$

$- x + 8 y = (- 1) (0)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 1$ by $0$ .

$x + 4 y = 6$

$- x + 8 y = 0$

$x + 4 y = 6$

$- x + 8 y = 0$

$x + 4 y = 6$

$- x + 8 y = 0$

Step 4

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

		$x$	$+$	$4$	$y$	$=$	$6$
$+$	$-$	$x$	$+$	$8$	$y$	$=$	$0$
			$1$	$2$	$y$	$=$	$6$

Step 5

Divide each term in $12 y = 6$ by $12$ and simplify.

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Step 5.1

Divide each term in $12 y = 6$ by $12$ .

$\frac{12 y}{12} = \frac{6}{12}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $12$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{6}{12}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{12}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $6$ and $12$ .

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Step 5.3.1.1

Factor $6$ out of $6$ .

$y = \frac{6 (1)}{12}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $6$ out of $12$ .

$y = \frac{6 \cdot 1}{6 \cdot 2}$

Step 5.3.1.2.2

Cancel the common factor.

$y = \frac{6 \cdot 1}{6 \cdot 2}$

Step 5.3.1.2.3

Rewrite the expression.

$y = \frac{1}{2}$

Step 6

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

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Step 6.1

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$x + 4 (\frac{1}{2}) = 6$

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Factor $2$ out of $4$ .

$x + 2 (2) \frac{1}{2} = 6$

Step 6.2.2

Cancel the common factor.

$x + 2 \cdot 2 \frac{1}{2} = 6$

Step 6.2.3

Rewrite the expression.

$x + 2 = 6$

Step 6.3

Move all terms not containing $x$ to the right side of the equation.

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Step 6.3.1

Subtract $2$ from both sides of the equation.

$x = 6 - 2$

Step 6.3.2

Subtract $2$ from $6$ .

$x = 4$

Step 7

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

$(4, \frac{1}{2})$

Step 8

The result can be shown in multiple forms.

Point Form:

$(4, \frac{1}{2})$

Equation Form:

$x = 4, y = \frac{1}{2}$

Step 9