Algebra Examples

$4 x + 7 y = 47$ $5 x - 4 y = - 5$

Step 1

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

$(- 5) \cdot (4 x + 7 y) = (- 5) (47)$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(- 5) \cdot (4 x + 7 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$- 5 (4 x) - 5 (7 y) = (- 5) (47)$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $4$ by $- 5$ .

$- 20 x - 5 (7 y) = (- 5) (47)$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

Step 2.1.1.2.2

Multiply $7$ by $- 5$ .

$- 20 x - 35 y = (- 5) (47)$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

$- 20 x - 35 y = (- 5) (47)$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

$- 20 x - 35 y = (- 5) (47)$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

$- 20 x - 35 y = (- 5) (47)$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 5$ by $47$ .

$- 20 x - 35 y = - 235$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

$- 20 x - 35 y = - 235$

$(4) \cdot (5 x - 4 y) = (4) (- 5)$

Step 2.3

Simplify the left side.

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Step 2.3.1

Simplify $(4) \cdot (5 x - 4 y)$ .

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Step 2.3.1.1

Apply the distributive property.

$- 20 x - 35 y = - 235$

$4 (5 x) + 4 (- 4 y) = (4) (- 5)$

Step 2.3.1.2

Multiply.

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Step 2.3.1.2.1

Multiply $5$ by $4$ .

$- 20 x - 35 y = - 235$

$20 x + 4 (- 4 y) = (4) (- 5)$

Step 2.3.1.2.2

Multiply $- 4$ by $4$ .

$- 20 x - 35 y = - 235$

$20 x - 16 y = (4) (- 5)$

$- 20 x - 35 y = - 235$

$20 x - 16 y = (4) (- 5)$

$- 20 x - 35 y = - 235$

$20 x - 16 y = (4) (- 5)$

$- 20 x - 35 y = - 235$

$20 x - 16 y = (4) (- 5)$

Step 2.4

Simplify the right side.

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Step 2.4.1

Multiply $4$ by $- 5$ .

$- 20 x - 35 y = - 235$

$20 x - 16 y = - 20$

$- 20 x - 35 y = - 235$

$20 x - 16 y = - 20$

$- 20 x - 35 y = - 235$

$20 x - 16 y = - 20$

Step 3

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

	$-$	$2$	$0$	$x$	$-$	$3$	$5$	$y$	$=$	$-$	$2$	$3$	$5$
$+$		$2$	$0$	$x$	$-$	$1$	$6$	$y$	$=$		$-$	$2$	$0$
					$-$	$5$	$1$	$y$	$=$	$-$	$2$	$5$	$5$

Step 4

Divide each term in $- 51 y = - 255$ by $- 51$ and simplify.

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Step 4.1

Divide each term in $- 51 y = - 255$ by $- 51$ .

$\frac{- 51 y}{- 51} = \frac{- 255}{- 51}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 51$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 51 y}{- 51} = \frac{- 255}{- 51}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 255}{- 51}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 255$ by $- 51$ .

$y = 5$

Step 5

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

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Step 5.1

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

$- 20 x - 35 \cdot 5 = - 235$

Step 5.2

Multiply $- 35$ by $5$ .

$- 20 x - 175 = - 235$

Step 5.3

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

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Step 5.3.1

Add $175$ to both sides of the equation.

$- 20 x = - 235 + 175$

Step 5.3.2

Add $- 235$ and $175$ .

$- 20 x = - 60$

Step 5.4

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

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Step 5.4.1

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

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

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.

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

Step 5.4.2.1.2

Divide $x$ by $1$ .

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

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Divide $- 60$ by $- 20$ .

$x = 3$

Step 6

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

$(3, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(3, 5)$

Equation Form:

$x = 3, y = 5$

Step 8

	$-$	$2$	$0$	$x$	$-$	$3$	$5$	$y$	$=$	$-$	$2$	$3$	$5$
$+$		$2$	$0$	$x$	$-$	$1$	$6$	$y$	$=$		$-$	$2$	$0$
					$-$	$5$	$1$	$y$	$=$	$-$	$2$	$5$	$5$

	$-$	$2$	$0$	$x$	$-$	$3$	$5$	$y$	$=$	$-$	$2$	$3$	$5$
$+$		$2$	$0$	$x$	$-$	$1$	$6$	$y$	$=$		$-$	$2$	$0$
					$-$	$5$	$1$	$y$	$=$	$-$	$2$	$5$	$5$

	$-$	$2$	$0$	$x$	$-$	$3$	$5$	$y$	$=$	$-$	$2$	$3$	$5$
$+$		$2$	$0$	$x$	$-$	$1$	$6$	$y$	$=$		$-$	$2$	$0$
					$-$	$5$	$1$	$y$	$=$	$-$	$2$	$5$	$5$