Solve by Addition/Elimination -16+20x-8y=0 36=-18y-22x

$- 16 + 20 x - 8 y = 0$ $36 = - 18 y - 22 x$

Step 1

Simplify the left side.

Move $- 16$ .

$20 x - 8 y - 16 = 0$

$36 = - 18 y - 22 x$

$20 x - 8 y - 16 = 0$

$36 = - 18 y - 22 x$

Step 2

Simplify the right side.

Reorder $- 18 y$ and $- 22 x$ .

$36 = - 22 x - 18 y$

$20 x - 8 y - 16 = 0$

$36 = - 22 x - 18 y$

$20 x - 8 y - 16 = 0$

Step 3

Move all terms containing variables to the left.

Add $16$ to both sides of the equation.

$20 x - 8 y = 16, 36 = - 22 x - 18 y$

Subtract $36$ from both sides of the equation.

$20 x - 8 y = 16, 0 = - 22 x - 18 y - 36$

Move all terms containing variables to the left side of the equation.

Add $22 x$ to both sides of the equation.

$20 x - 8 y = 16, 22 x = - 18 y - 36$

Add $18 y$ to both sides of the equation.

$20 x - 8 y = 16, 22 x + 18 y = - 36$

Step 4

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

$(9) \cdot (20 x - 8 y) = (9) (16)$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

Step 5

Simplify.

Simplify the left side.

Simplify $(9) \cdot (20 x - 8 y)$ .

Apply the distributive property.

$9 (20 x) + 9 (- 8 y) = (9) (16)$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

Multiply.

Multiply $20$ by $9$ .

$180 x + 9 (- 8 y) = (9) (16)$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

Multiply $- 8$ by $9$ .

$180 x - 72 y = (9) (16)$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

$180 x - 72 y = (9) (16)$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

$180 x - 72 y = (9) (16)$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

$180 x - 72 y = (9) (16)$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

Simplify the right side.

Multiply $9$ by $16$ .

$180 x - 72 y = 144$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

$180 x - 72 y = 144$

$(4) \cdot (22 x + 18 y) = (4) (- 36)$

Simplify the left side.

Simplify $(4) \cdot (22 x + 18 y)$ .

Apply the distributive property.

$180 x - 72 y = 144$

$4 (22 x) + 4 (18 y) = (4) (- 36)$

Multiply.

Multiply $22$ by $4$ .

$180 x - 72 y = 144$

$88 x + 4 (18 y) = (4) (- 36)$

Multiply $18$ by $4$ .

$180 x - 72 y = 144$

$88 x + 72 y = (4) (- 36)$

$180 x - 72 y = 144$

$88 x + 72 y = (4) (- 36)$

$180 x - 72 y = 144$

$88 x + 72 y = (4) (- 36)$

$180 x - 72 y = 144$

$88 x + 72 y = (4) (- 36)$

Simplify the right side.

Multiply $4$ by $- 36$ .

$180 x - 72 y = 144$

$88 x + 72 y = - 144$

$180 x - 72 y = 144$

$88 x + 72 y = - 144$

$180 x - 72 y = 144$

$88 x + 72 y = - 144$

Step 6

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

	$1$	$8$	$0$	$x$	$-$	$7$	$2$	$y$	$=$		$1$	$4$	$4$
$+$		$8$	$8$	$x$	$+$	$7$	$2$	$y$	$=$	$-$	$1$	$4$	$4$
	$2$	$6$	$8$	$x$					$=$				$0$

Step 7

Divide each term in $268 x = 0$ by $268$ and simplify.

Divide each term in $268 x = 0$ by $268$ .

$\frac{268 x}{268} = \frac{0}{268}$

Simplify the left side.

Cancel the common factor of $268$ .

Cancel the common factor.

$\frac{268 x}{268} = \frac{0}{268}$

Divide $x$ by $1$ .

$x = \frac{0}{268}$

Simplify the right side.

Divide $0$ by $268$ .

$x = 0$

Step 8

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

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

$180 (0) - 72 y = 144$

Simplify $180 (0) - 72 y$ .

Multiply $180$ by $0$ .

$0 - 72 y = 144$

Subtract $72 y$ from $0$ .

$- 72 y = 144$

Divide each term in $- 72 y = 144$ by $- 72$ and simplify.

Divide each term in $- 72 y = 144$ by $- 72$ .

$\frac{- 72 y}{- 72} = \frac{144}{- 72}$

Simplify the left side.

Cancel the common factor of $- 72$ .

Cancel the common factor.

$\frac{- 72 y}{- 72} = \frac{144}{- 72}$

Divide $y$ by $1$ .

$y = \frac{144}{- 72}$

Simplify the right side.

Divide $144$ by $- 72$ .

$y = - 2$

Step 9

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

$(0, - 2)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(0, - 2)$

Equation Form:

$x = 0, y = - 2$

Step 11

Solve by Addition/Elimination -16+20x-8y=0 36=-18y-22x

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