Algebra Examples

$11 x = 57 - 2 y$ $4 (x - 2 y) = 11 + y$

Step 1

Simplify the right side.

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Step 1.1

Reorder $57$ and $- 2 y$ .

$11 x = - 2 y + 57$

$4 (x - 2 y) = 11 + y$

$11 x = - 2 y + 57$

$4 (x - 2 y) = 11 + y$

Step 2

Simplify the left side.

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Step 2.1

Simplify $4 (x - 2 y)$ .

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Step 2.1.1

Apply the distributive property.

$4 x + 4 (- 2 y) = 11 + y$

$11 x = - 2 y + 57$

Step 2.1.2

Multiply $- 2$ by $4$ .

$4 x - 8 y = 11 + y$

$11 x = - 2 y + 57$

$4 x - 8 y = 11 + y$

$11 x = - 2 y + 57$

$4 x - 8 y = 11 + y$

$11 x = - 2 y + 57$

Step 3

Simplify the right side.

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Step 3.1

Reorder $11$ and $y$ .

$4 x - 8 y = y + 11$

$11 x = - 2 y + 57$

$4 x - 8 y = y + 11$

$11 x = - 2 y + 57$

Step 4

Move all terms containing variables to the left.

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Step 4.1

Add $2 y$ to both sides of the equation.

$11 x + 2 y = 57, 4 x - 8 y = y + 11$

Step 4.2

Move all terms containing variables to the left side of the equation.

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Step 4.2.1

Subtract $y$ from both sides of the equation.

$11 x + 2 y = 57, 4 x - 8 y - y = 11$

Step 4.2.2

Subtract $y$ from $- 8 y$ .

$11 x + 2 y = 57, 4 x - 9 y = 11$

Step 5

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

$(9) \cdot (11 x + 2 y) = (9) (57)$

$(2) \cdot (4 x - 9 y) = (2) (11)$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $(9) \cdot (11 x + 2 y)$ .

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Step 6.1.1.1

Apply the distributive property.

$9 (11 x) + 9 (2 y) = (9) (57)$

$(2) \cdot (4 x - 9 y) = (2) (11)$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $11$ by $9$ .

$99 x + 9 (2 y) = (9) (57)$

$(2) \cdot (4 x - 9 y) = (2) (11)$

Step 6.1.1.2.2

Multiply $2$ by $9$ .

$99 x + 18 y = (9) (57)$

$(2) \cdot (4 x - 9 y) = (2) (11)$

$99 x + 18 y = (9) (57)$

$(2) \cdot (4 x - 9 y) = (2) (11)$

$99 x + 18 y = (9) (57)$

$(2) \cdot (4 x - 9 y) = (2) (11)$

$99 x + 18 y = (9) (57)$

$(2) \cdot (4 x - 9 y) = (2) (11)$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $9$ by $57$ .

$99 x + 18 y = 513$

$(2) \cdot (4 x - 9 y) = (2) (11)$

$99 x + 18 y = 513$

$(2) \cdot (4 x - 9 y) = (2) (11)$

Step 6.3

Simplify the left side.

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Step 6.3.1

Simplify $(2) \cdot (4 x - 9 y)$ .

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Step 6.3.1.1

Apply the distributive property.

$99 x + 18 y = 513$

$2 (4 x) + 2 (- 9 y) = (2) (11)$

Step 6.3.1.2

Multiply.

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Step 6.3.1.2.1

Multiply $4$ by $2$ .

$99 x + 18 y = 513$

$8 x + 2 (- 9 y) = (2) (11)$

Step 6.3.1.2.2

Multiply $- 9$ by $2$ .

$99 x + 18 y = 513$

$8 x - 18 y = (2) (11)$

$99 x + 18 y = 513$

$8 x - 18 y = (2) (11)$

$99 x + 18 y = 513$

$8 x - 18 y = (2) (11)$

$99 x + 18 y = 513$

$8 x - 18 y = (2) (11)$

Step 6.4

Simplify the right side.

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Step 6.4.1

Multiply $2$ by $11$ .

$99 x + 18 y = 513$

$8 x - 18 y = 22$

$99 x + 18 y = 513$

$8 x - 18 y = 22$

$99 x + 18 y = 513$

$8 x - 18 y = 22$

Step 7

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

	$9$	$9$	$x$		$+$	$1$	$8$	$y$	$=$	$5$	$1$	$3$
$+$			$8$	$x$	$-$	$1$	$8$	$y$	$=$		$2$	$2$
	$1$	$0$	$7$	$x$					$=$	$5$	$3$	$5$

Step 8

Divide each term in $107 x = 535$ by $107$ and simplify.

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Step 8.1

Divide each term in $107 x = 535$ by $107$ .

$\frac{107 x}{107} = \frac{535}{107}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $107$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{107 x}{107} = \frac{535}{107}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x = \frac{535}{107}$

Step 8.3

Simplify the right side.

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Step 8.3.1

Divide $535$ by $107$ .

$x = 5$

Step 9

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

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Step 9.1

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

$99 (5) + 18 y = 513$

Step 9.2

Multiply $99$ by $5$ .

$495 + 18 y = 513$

Step 9.3

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

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Step 9.3.1

Subtract $495$ from both sides of the equation.

$18 y = 513 - 495$

Step 9.3.2

Subtract $495$ from $513$ .

$18 y = 18$

Step 9.4

Divide each term in $18 y = 18$ by $18$ and simplify.

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Step 9.4.1

Divide each term in $18 y = 18$ by $18$ .

$\frac{18 y}{18} = \frac{18}{18}$

Step 9.4.2

Simplify the left side.

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Step 9.4.2.1

Cancel the common factor of $18$ .

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Step 9.4.2.1.1

Cancel the common factor.

$\frac{18 y}{18} = \frac{18}{18}$

Step 9.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{18}$

Step 9.4.3

Simplify the right side.

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Step 9.4.3.1

Divide $18$ by $18$ .

$y = 1$

Step 10

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

$(5, 1)$

Step 11

The result can be shown in multiple forms.

Point Form:

$(5, 1)$

Equation Form:

$x = 5, y = 1$

Step 12

	$9$	$9$	$x$		$+$	$1$	$8$	$y$	$=$	$5$	$1$	$3$
$+$			$8$	$x$	$-$	$1$	$8$	$y$	$=$		$2$	$2$
	$1$	$0$	$7$	$x$					$=$	$5$	$3$	$5$

	$9$	$9$	$x$		$+$	$1$	$8$	$y$	$=$	$5$	$1$	$3$
$+$			$8$	$x$	$-$	$1$	$8$	$y$	$=$		$2$	$2$
	$1$	$0$	$7$	$x$					$=$	$5$	$3$	$5$

	$9$	$9$	$x$		$+$	$1$	$8$	$y$	$=$	$5$	$1$	$3$
$+$			$8$	$x$	$-$	$1$	$8$	$y$	$=$		$2$	$2$
	$1$	$0$	$7$	$x$					$=$	$5$	$3$	$5$