Solve by Addition/Elimination 3x+3y=-9 3x-3y=21

$3 x + 3 y = - 9$ $3 x - 3 y = 21$

Step 1

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

$(- 1) \cdot (3 x + 3 y) = (- 1) (- 9)$

$3 x - 3 y = 21$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (3 x + 3 y)$ .

Apply the distributive property.

$- 1 (3 x) - 1 (3 y) = (- 1) (- 9)$

$3 x - 3 y = 21$

Multiply.

Multiply $3$ by $- 1$ .

$- 3 x - 1 (3 y) = (- 1) (- 9)$

$3 x - 3 y = 21$

Multiply $3$ by $- 1$ .

$- 3 x - 3 y = (- 1) (- 9)$

$3 x - 3 y = 21$

$- 3 x - 3 y = (- 1) (- 9)$

$3 x - 3 y = 21$

$- 3 x - 3 y = (- 1) (- 9)$

$3 x - 3 y = 21$

$- 3 x - 3 y = (- 1) (- 9)$

$3 x - 3 y = 21$

Simplify the right side.

Multiply $- 1$ by $- 9$ .

$- 3 x - 3 y = 9$

$3 x - 3 y = 21$

$- 3 x - 3 y = 9$

$3 x - 3 y = 21$

$- 3 x - 3 y = 9$

$3 x - 3 y = 21$

Step 3

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

	$-$	$3$	$x$	$-$	$3$	$y$	$=$		$9$
$+$		$3$	$x$	$-$	$3$	$y$	$=$	$2$	$1$
				$-$	$6$	$y$	$=$	$3$	$0$

Step 4

Divide each term in $- 6 y = 30$ by $- 6$ and simplify.

Divide each term in $- 6 y = 30$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{30}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{30}{- 6}$

Divide $y$ by $1$ .

$y = \frac{30}{- 6}$

Simplify the right side.

Divide $30$ by $- 6$ .

$y = - 5$

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 $x$ .

$- 3 x - 3 \cdot - 5 = 9$

Multiply $- 3$ by $- 5$ .

$- 3 x + 15 = 9$

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

Subtract $15$ from both sides of the equation.

$- 3 x = 9 - 15$

Subtract $15$ from $9$ .

$- 3 x = - 6$

Divide each term in $- 3 x = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 6$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x = 2$

Step 6

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

$(2, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 5)$

Equation Form:

$x = 2, y = - 5$

Step 8

Solve by Addition/Elimination 3x+3y=-9 3x-3y=21

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