Solve by Addition/Elimination x-y=2 3x+2y=-9

$x - y = 2$ $3 x + 2 y = - 9$

Step 1

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

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

$3 x + 2 y = - 9$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$3 x + 2 y = - 9$

Multiply $- 1$ by $2$ .

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

$3 x + 2 y = - 9$

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

$3 x + 2 y = - 9$

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

$3 x + 2 y = - 9$

Simplify the right side.

Multiply $2$ by $2$ .

$2 x - 2 y = 4$

$3 x + 2 y = - 9$

$2 x - 2 y = 4$

$3 x + 2 y = - 9$

$2 x - 2 y = 4$

$3 x + 2 y = - 9$

Step 3

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

	$2$	$x$	$-$	$2$	$y$	$=$		$4$
$+$	$3$	$x$	$+$	$2$	$y$	$=$	$-$	$9$
	$5$	$x$				$=$	$-$	$5$

Step 4

Divide each term in $5 x = - 5$ by $5$ and simplify.

Divide each term in $5 x = - 5$ by $5$ .

$\frac{5 x}{5} = \frac{- 5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 5}{5}$

Divide $x$ by $1$ .

$x = \frac{- 5}{5}$

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

Step 5

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 $y$ .

$2 (- 1) - 2 y = 4$

Multiply $2$ by $- 1$ .

$- 2 - 2 y = 4$

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

Add $2$ to both sides of the equation.

$- 2 y = 4 + 2$

Add $4$ and $2$ .

$- 2 y = 6$

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 6

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

$(- 1, - 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, - 3)$

Equation Form:

$x = - 1, y = - 3$

Step 8

Solve by Addition/Elimination x-y=2 3x+2y=-9

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