Algebra Examples

$x + y - 6 = 0$ $x - y - 8 = 0$

Add $6$ to both sides of the equation.

$x + y = 6$

$x - y - 8 = 0$

Add $8$ to both sides of the equation.

$x - y = 8$

$x + y = 6$

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

$x + y = 6$

$(- 1) \cdot (x - y) = (- 1) (8)$

Simplify.

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Simplify the left side.

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Simplify $(- 1) \cdot (x - y)$ .

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Apply the distributive property.

$x + y = 6$

$- 1 x - 1 (- y) = (- 1) (8)$

Rewrite $- 1 x$ as $- x$ .

$x + y = 6$

$- x - 1 (- y) = (- 1) (8)$

Multiply $- 1 (- y)$ .

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Multiply $- 1$ by $- 1$ .

$x + y = 6$

$- x + 1 y = (- 1) (8)$

Multiply $y$ by $1$ .

$x + y = 6$

$- x + y = (- 1) (8)$

$x + y = 6$

$- x + y = (- 1) (8)$

$x + y = 6$

$- x + y = (- 1) (8)$

$x + y = 6$

$- x + y = (- 1) (8)$

Simplify the right side.

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Multiply $- 1$ by $8$ .

$x + y = 6$

$- x + y = - 8$

$x + y = 6$

$- x + y = - 8$

$x + y = 6$

$- x + y = - 8$

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

		$x$	$+$	$y$	$=$		$6$
$+$	$-$	$x$	$+$	$y$	$=$	$-$	$8$
			$2$	$y$	$=$	$-$	$2$

Divide each term in $2 y = - 2$ by $2$ and simplify.

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Divide each term in $2 y = - 2$ by $2$ .

$\frac{2 y}{2} = \frac{- 2}{2}$

Simplify the left side.

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Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2}{2}$

Divide $y$ by $1$ .

$y = \frac{- 2}{2}$

Simplify the right side.

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Divide $- 2$ by $2$ .

$y = - 1$

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

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

$x - 1 = 6$

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

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Add $1$ to both sides of the equation.

$x = 6 + 1$

Add $6$ and $1$ .

$x = 7$

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

$(7, - 1)$

The result can be shown in multiple forms.

Point Form:

$(7, - 1)$

Equation Form:

$x = 7, y = - 1$