Algebra Examples

$- y - 10 = 6 x$ $5 x + y = - 10$

Step 1

Move all terms containing variables to the left.

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Step 1.1

Add $10$ to both sides of the equation.

$- y = 6 x + 10, 5 x + y = - 10$

Step 1.2

Subtract $6 x$ from both sides of the equation.

$- y - 6 x = 10, 5 x + y = - 10$

Step 2

Reorder the polynomial.

$- 6 x - y = 10$

$5 x + y = - 10$

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

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

Step 4.2.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $- 1$ .

$x = 0$

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 $y$ .

$- 6 \cdot 0 - y = 10$

Step 5.2

Simplify $- 6 \cdot 0 - y$ .

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Step 5.2.1

Multiply $- 6$ by $0$ .

$0 - y = 10$

Step 5.2.2

Subtract $y$ from $0$ .

$- y = 10$

Step 5.3

Divide each term in $- y = 10$ by $- 1$ and simplify.

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Step 5.3.1

Divide each term in $- y = 10$ by $- 1$ .

$\frac{- y}{- 1} = \frac{10}{- 1}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{10}{- 1}$

Step 5.3.2.2

Divide $y$ by $1$ .

$y = \frac{10}{- 1}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $10$ by $- 1$ .

$y = - 10$

Step 6

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

$(0, - 10)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(0, - 10)$

Equation Form:

$x = 0, y = - 10$

Step 8

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

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

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