Algebra Examples

$11 x - 20 y = 28$ and $3 x + 4 y = 36$

Step 1

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

$11 x - 20 y = 28$

$(5) \cdot (3 x + 4 y) = (5) (36)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(5) \cdot (3 x + 4 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$11 x - 20 y = 28$

$5 (3 x) + 5 (4 y) = (5) (36)$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $3$ by $5$ .

$11 x - 20 y = 28$

$15 x + 5 (4 y) = (5) (36)$

Step 2.1.1.2.2

Multiply $4$ by $5$ .

$11 x - 20 y = 28$

$15 x + 20 y = (5) (36)$

$11 x - 20 y = 28$

$15 x + 20 y = (5) (36)$

$11 x - 20 y = 28$

$15 x + 20 y = (5) (36)$

$11 x - 20 y = 28$

$15 x + 20 y = (5) (36)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $36$ .

$11 x - 20 y = 28$

$15 x + 20 y = 180$

$11 x - 20 y = 28$

$15 x + 20 y = 180$

$11 x - 20 y = 28$

$15 x + 20 y = 180$

Step 3

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

	$1$	$1$	$x$	$-$	$2$	$0$	$y$	$=$		$2$	$8$
$+$	$1$	$5$	$x$	$+$	$2$	$0$	$y$	$=$	$1$	$8$	$0$
	$2$	$6$	$x$					$=$	$2$	$0$	$8$

Step 4

Divide each term in $26 x = 208$ by $26$ and simplify.

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Step 4.1

Divide each term in $26 x = 208$ by $26$ .

$\frac{26 x}{26} = \frac{208}{26}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $26$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{26 x}{26} = \frac{208}{26}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{208}{26}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $208$ by $26$ .

$x = 8$

Step 5

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

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Step 5.1

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

$11 (8) - 20 y = 28$

Step 5.2

Multiply $11$ by $8$ .

$88 - 20 y = 28$

Step 5.3

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

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Step 5.3.1

Subtract $88$ from both sides of the equation.

$- 20 y = 28 - 88$

Step 5.3.2

Subtract $88$ from $28$ .

$- 20 y = - 60$

Step 5.4

Divide each term in $- 20 y = - 60$ by $- 20$ and simplify.

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Step 5.4.1

Divide each term in $- 20 y = - 60$ by $- 20$ .

$\frac{- 20 y}{- 20} = \frac{- 60}{- 20}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of $- 20$ .

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Step 5.4.2.1.1

Cancel the common factor.

$\frac{- 20 y}{- 20} = \frac{- 60}{- 20}$

Step 5.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 60}{- 20}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $- 60$ by $- 20$ .

$y = 3$

Step 6

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

$(8, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(8, 3)$

Equation Form:

$x = 8, y = 3$

Step 8

	$1$	$1$	$x$	$-$	$2$	$0$	$y$	$=$		$2$	$8$
$+$	$1$	$5$	$x$	$+$	$2$	$0$	$y$	$=$	$1$	$8$	$0$
	$2$	$6$	$x$					$=$	$2$	$0$	$8$

	$1$	$1$	$x$	$-$	$2$	$0$	$y$	$=$		$2$	$8$
$+$	$1$	$5$	$x$	$+$	$2$	$0$	$y$	$=$	$1$	$8$	$0$
	$2$	$6$	$x$					$=$	$2$	$0$	$8$

	$1$	$1$	$x$	$-$	$2$	$0$	$y$	$=$		$2$	$8$
$+$	$1$	$5$	$x$	$+$	$2$	$0$	$y$	$=$	$1$	$8$	$0$
	$2$	$6$	$x$					$=$	$2$	$0$	$8$