Algebra Examples

$x - y = 4$ $x - 2 y = 10$

Step 1

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

$x - y = 4$

$(- 1) \cdot (x - 2 y) = (- 1) (10)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(- 1) \cdot (x - 2 y)$ .

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Step 2.1.1.1

Apply the distributive property.

$x - y = 4$

$- 1 x - 1 (- 2 y) = (- 1) (10)$

Step 2.1.1.2

Simplify the expression.

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Step 2.1.1.2.1

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

$x - y = 4$

$- x - 1 (- 2 y) = (- 1) (10)$

Step 2.1.1.2.2

Multiply $- 2$ by $- 1$ .

$x - y = 4$

$- x + 2 y = (- 1) (10)$

$x - y = 4$

$- x + 2 y = (- 1) (10)$

$x - y = 4$

$- x + 2 y = (- 1) (10)$

$x - y = 4$

$- x + 2 y = (- 1) (10)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 1$ by $10$ .

$x - y = 4$

$- x + 2 y = - 10$

$x - y = 4$

$- x + 2 y = - 10$

$x - y = 4$

$- x + 2 y = - 10$

Step 3

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

		$x$		$-$	$y$	$=$			$4$
$+$	$-$	$x$	$+$	$2$	$y$	$=$	$-$	$1$	$0$
					$y$	$=$		$-$	$6$

Step 4

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

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Step 4.1

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

$x - (- 6) = 4$

Step 4.2

Multiply $- 1$ by $- 6$ .

$x + 6 = 4$

Step 4.3

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

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Step 4.3.1

Subtract $6$ from both sides of the equation.

$x = 4 - 6$

Step 4.3.2

Subtract $6$ from $4$ .

$x = - 2$

Step 5

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

$(- 2, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, - 6)$

Equation Form:

$x = - 2, y = - 6$

Step 7