Solve by Addition/Elimination x+2y=8 -2x-2y=-10

$x + 2 y = 8$ $- 2 x - 2 y = - 10$

Step 1

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

$(2) \cdot (x + 2 y) = (2) (8)$

$- 2 x - 2 y = - 10$

Step 2

Simplify.

Simplify the left side.

Simplify $(2) \cdot (x + 2 y)$ .

Apply the distributive property.

$2 x + 2 (2 y) = (2) (8)$

$- 2 x - 2 y = - 10$

Multiply $2$ by $2$ .

$2 x + 4 y = (2) (8)$

$- 2 x - 2 y = - 10$

$2 x + 4 y = (2) (8)$

$- 2 x - 2 y = - 10$

$2 x + 4 y = (2) (8)$

$- 2 x - 2 y = - 10$

Simplify the right side.

Multiply $2$ by $8$ .

$2 x + 4 y = 16$

$- 2 x - 2 y = - 10$

$2 x + 4 y = 16$

$- 2 x - 2 y = - 10$

$2 x + 4 y = 16$

$- 2 x - 2 y = - 10$

Step 3

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

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

Step 4

Divide each term in $2 y = 6$ by $2$ and simplify.

Divide each term in $2 y = 6$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$y = 3$

Step 5

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

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

$2 x + 4 (3) = 16$

Multiply $4$ by $3$ .

$2 x + 12 = 16$

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

Subtract $12$ from both sides of the equation.

$2 x = 16 - 12$

Subtract $12$ from $16$ .

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

Step 6

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

$(2, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 8

Solve by Addition/Elimination x+2y=8 -2x-2y=-10

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