Algebra Examples

$- 6 y + 11 x = - 36$ $- 4 y + 7 x = - 24$

Step 1

Simplify the left side.

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Step 1.1

Reorder $- 6 y$ and $11 x$ .

$11 x - 6 y = - 36$

$- 4 y + 7 x = - 24$

$11 x - 6 y = - 36$

$- 4 y + 7 x = - 24$

Step 2

Simplify the left side.

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Step 2.1

Reorder $- 4 y$ and $7 x$ .

$7 x - 4 y = - 24$

$11 x - 6 y = - 36$

$7 x - 4 y = - 24$

$11 x - 6 y = - 36$

Step 3

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

$(- 2) \cdot (11 x - 6 y) = (- 2) (- 36)$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $(- 2) \cdot (11 x - 6 y)$ .

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Step 4.1.1.1

Apply the distributive property.

$- 2 (11 x) - 2 (- 6 y) = (- 2) (- 36)$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $11$ by $- 2$ .

$- 22 x - 2 (- 6 y) = (- 2) (- 36)$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

Step 4.1.1.2.2

Multiply $- 6$ by $- 2$ .

$- 22 x + 12 y = (- 2) (- 36)$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

$- 22 x + 12 y = (- 2) (- 36)$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

$- 22 x + 12 y = (- 2) (- 36)$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

$- 22 x + 12 y = (- 2) (- 36)$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 2$ by $- 36$ .

$- 22 x + 12 y = 72$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

$- 22 x + 12 y = 72$

$(3) \cdot (7 x - 4 y) = (3) (- 24)$

Step 4.3

Simplify the left side.

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Step 4.3.1

Simplify $(3) \cdot (7 x - 4 y)$ .

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Step 4.3.1.1

Apply the distributive property.

$- 22 x + 12 y = 72$

$3 (7 x) + 3 (- 4 y) = (3) (- 24)$

Step 4.3.1.2

Multiply.

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Step 4.3.1.2.1

Multiply $7$ by $3$ .

$- 22 x + 12 y = 72$

$21 x + 3 (- 4 y) = (3) (- 24)$

Step 4.3.1.2.2

Multiply $- 4$ by $3$ .

$- 22 x + 12 y = 72$

$21 x - 12 y = (3) (- 24)$

$- 22 x + 12 y = 72$

$21 x - 12 y = (3) (- 24)$

$- 22 x + 12 y = 72$

$21 x - 12 y = (3) (- 24)$

$- 22 x + 12 y = 72$

$21 x - 12 y = (3) (- 24)$

Step 4.4

Simplify the right side.

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Step 4.4.1

Multiply $3$ by $- 24$ .

$- 22 x + 12 y = 72$

$21 x - 12 y = - 72$

$- 22 x + 12 y = 72$

$21 x - 12 y = - 72$

$- 22 x + 12 y = 72$

$21 x - 12 y = - 72$

Step 5

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

	$-$	$2$	$2$	$x$	$+$	$1$	$2$	$y$	$=$		$7$	$2$
$+$		$2$	$1$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$7$	$2$
			$-$	$x$					$=$			$0$

Step 6

Divide each term in $- x = 0$ by $- 1$ and simplify.

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Step 6.1

Divide each term in $- x = 0$ by $- 1$ .

$\frac{- x}{- 1} = \frac{0}{- 1}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{0}{- 1}$

Step 6.2.2

Divide $x$ by $1$ .

$x = \frac{0}{- 1}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $0$ by $- 1$ .

$x = 0$

Step 7

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

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Step 7.1

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

$- 22 \cdot 0 + 12 y = 72$

Step 7.2

Simplify $- 22 \cdot 0 + 12 y$ .

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Step 7.2.1

Multiply $- 22$ by $0$ .

$0 + 12 y = 72$

Step 7.2.2

Add $0$ and $12 y$ .

$12 y = 72$

Step 7.3

Divide each term in $12 y = 72$ by $12$ and simplify.

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Step 7.3.1

Divide each term in $12 y = 72$ by $12$ .

$\frac{12 y}{12} = \frac{72}{12}$

Step 7.3.2

Simplify the left side.

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Step 7.3.2.1

Cancel the common factor of $12$ .

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Step 7.3.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{72}{12}$

Step 7.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{72}{12}$

Step 7.3.3

Simplify the right side.

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Step 7.3.3.1

Divide $72$ by $12$ .

$y = 6$

Step 8

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

$(0, 6)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(0, 6)$

Equation Form:

$x = 0, y = 6$

Step 10

	$-$	$2$	$2$	$x$	$+$	$1$	$2$	$y$	$=$		$7$	$2$
$+$		$2$	$1$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$7$	$2$
			$-$	$x$					$=$			$0$

	$-$	$2$	$2$	$x$	$+$	$1$	$2$	$y$	$=$		$7$	$2$
$+$		$2$	$1$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$7$	$2$
			$-$	$x$					$=$			$0$

	$-$	$2$	$2$	$x$	$+$	$1$	$2$	$y$	$=$		$7$	$2$
$+$		$2$	$1$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$7$	$2$
			$-$	$x$					$=$			$0$