Algebra Examples

$7 y + 13 = - 5 x$ $5 x = 8 y - 28$

Step 1

Move all terms containing variables to the left.

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Step 1.1

Subtract $13$ from both sides of the equation.

$7 y = - 5 x - 13, 5 x = 8 y - 28$

Step 1.2

Add $5 x$ to both sides of the equation.

$7 y + 5 x = - 13, 5 x = 8 y - 28$

Step 1.3

Subtract $8 y$ from both sides of the equation.

$7 y + 5 x = - 13, 5 x - 8 y = - 28$

Step 2

Reorder the polynomial.

$5 x + 7 y = - 13$

$5 x - 8 y = - 28$

Step 3

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

$(- 1) \cdot (5 x + 7 y) = (- 1) (- 13)$

$5 x - 8 y = - 28$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $(- 1) \cdot (5 x + 7 y)$ .

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Step 4.1.1.1

Apply the distributive property.

$- 1 (5 x) - 1 (7 y) = (- 1) (- 13)$

$5 x - 8 y = - 28$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $5$ by $- 1$ .

$- 5 x - 1 (7 y) = (- 1) (- 13)$

$5 x - 8 y = - 28$

Step 4.1.1.2.2

Multiply $7$ by $- 1$ .

$- 5 x - 7 y = (- 1) (- 13)$

$5 x - 8 y = - 28$

$- 5 x - 7 y = (- 1) (- 13)$

$5 x - 8 y = - 28$

$- 5 x - 7 y = (- 1) (- 13)$

$5 x - 8 y = - 28$

$- 5 x - 7 y = (- 1) (- 13)$

$5 x - 8 y = - 28$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 1$ by $- 13$ .

$- 5 x - 7 y = 13$

$5 x - 8 y = - 28$

$- 5 x - 7 y = 13$

$5 x - 8 y = - 28$

$- 5 x - 7 y = 13$

$5 x - 8 y = - 28$

Step 5

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

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

Step 6

Divide each term in $- 15 y = - 15$ by $- 15$ and simplify.

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Step 6.1

Divide each term in $- 15 y = - 15$ by $- 15$ .

$\frac{- 15 y}{- 15} = \frac{- 15}{- 15}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 15$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 15 y}{- 15} = \frac{- 15}{- 15}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 15}{- 15}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 15$ by $- 15$ .

$y = 1$

Step 7

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

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Step 7.1

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

$- 5 x - 7 \cdot 1 = 13$

Step 7.2

Multiply $- 7$ by $1$ .

$- 5 x - 7 = 13$

Step 7.3

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

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Step 7.3.1

Add $7$ to both sides of the equation.

$- 5 x = 13 + 7$

Step 7.3.2

Add $13$ and $7$ .

$- 5 x = 20$

Step 7.4

Divide each term in $- 5 x = 20$ by $- 5$ and simplify.

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Step 7.4.1

Divide each term in $- 5 x = 20$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{20}{- 5}$

Step 7.4.2

Simplify the left side.

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Step 7.4.2.1

Cancel the common factor of $- 5$ .

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Step 7.4.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{20}{- 5}$

Step 7.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{- 5}$

Step 7.4.3

Simplify the right side.

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Step 7.4.3.1

Divide $20$ by $- 5$ .

$x = - 4$

Step 8

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

$(- 4, 1)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 4, 1)$

Equation Form:

$x = - 4, y = 1$

Step 10

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

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

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