Algebra Examples

$x - y = 19$ , $- 2 x + \frac{y}{6} = 28$

Step 1

Multiply each term in $- 2 x + \frac{y}{6} = 28$ by $6$ to eliminate the fractions.

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Step 1.1

Multiply each term in $- 2 x + \frac{y}{6} = 28$ by $6$ .

$- 2 x \cdot 6 + \frac{y}{6} \cdot 6 = 28 \cdot 6$

$x - y = 19$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $6$ by $- 2$ .

$- 12 x + \frac{y}{6} \cdot 6 = 28 \cdot 6$

$x - y = 19$

Step 1.2.1.2

Cancel the common factor of $6$ .

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Step 1.2.1.2.1

Cancel the common factor.

$- 12 x + \frac{y}{6} \cdot 6 = 28 \cdot 6$

$x - y = 19$

Step 1.2.1.2.2

Rewrite the expression.

$- 12 x + y = 28 \cdot 6$

$x - y = 19$

$- 12 x + y = 28 \cdot 6$

$x - y = 19$

$- 12 x + y = 28 \cdot 6$

$x - y = 19$

$- 12 x + y = 28 \cdot 6$

$x - y = 19$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $28$ by $6$ .

$- 12 x + y = 168$

$x - y = 19$

$- 12 x + y = 168$

$x - y = 19$

$- 12 x + y = 168$

$x - y = 19$

Step 2

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

				$x$	$-$	$y$	$=$		$1$	$9$
$+$	$-$	$1$	$2$	$x$	$+$	$y$	$=$	$1$	$6$	$8$
	$-$	$1$	$1$	$x$			$=$	$1$	$8$	$7$

Step 3

Divide each term in $- 11 x = 187$ by $- 11$ and simplify.

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Step 3.1

Divide each term in $- 11 x = 187$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{187}{- 11}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 11$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{187}{- 11}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{187}{- 11}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $187$ by $- 11$ .

$x = - 17$

Step 4

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

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Step 4.1

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

$(- 17) - y = 19$

Step 4.2

Remove parentheses.

$- 17 - y = 19$

Step 4.3

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

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Step 4.3.1

Add $17$ to both sides of the equation.

$- y = 19 + 17$

Step 4.3.2

Add $19$ and $17$ .

$- y = 36$

Step 4.4

Divide each term in $- y = 36$ by $- 1$ and simplify.

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Step 4.4.1

Divide each term in $- y = 36$ by $- 1$ .

$\frac{- y}{- 1} = \frac{36}{- 1}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{36}{- 1}$

Step 4.4.2.2

Divide $y$ by $1$ .

$y = \frac{36}{- 1}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide $36$ by $- 1$ .

$y = - 36$

Step 5

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

$(- 17, - 36)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 17, - 36)$

Equation Form:

$x = - 17, y = - 36$

Step 7

				$x$	$-$	$y$	$=$		$1$	$9$
$+$	$-$	$1$	$2$	$x$	$+$	$y$	$=$	$1$	$6$	$8$
	$-$	$1$	$1$	$x$			$=$	$1$	$8$	$7$

				$x$	$-$	$y$	$=$		$1$	$9$
$+$	$-$	$1$	$2$	$x$	$+$	$y$	$=$	$1$	$6$	$8$
	$-$	$1$	$1$	$x$			$=$	$1$	$8$	$7$

				$x$	$-$	$y$	$=$		$1$	$9$
$+$	$-$	$1$	$2$	$x$	$+$	$y$	$=$	$1$	$6$	$8$
	$-$	$1$	$1$	$x$			$=$	$1$	$8$	$7$