Solve by Addition/Elimination 3x-2y=-9 2x-3y=-16

$3 x - 2 y = - 9$ $2 x - 3 y = - 16$

Step 1

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

$(- 2) \cdot (3 x - 2 y) = (- 2) (- 9)$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (3 x - 2 y)$ .

Apply the distributive property.

$- 2 (3 x) - 2 (- 2 y) = (- 2) (- 9)$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

Multiply.

Multiply $3$ by $- 2$ .

$- 6 x - 2 (- 2 y) = (- 2) (- 9)$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

Multiply $- 2$ by $- 2$ .

$- 6 x + 4 y = (- 2) (- 9)$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

$- 6 x + 4 y = (- 2) (- 9)$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

$- 6 x + 4 y = (- 2) (- 9)$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

$- 6 x + 4 y = (- 2) (- 9)$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

Simplify the right side.

Multiply $- 2$ by $- 9$ .

$- 6 x + 4 y = 18$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

$- 6 x + 4 y = 18$

$(3) \cdot (2 x - 3 y) = (3) (- 16)$

Simplify the left side.

Simplify $(3) \cdot (2 x - 3 y)$ .

Apply the distributive property.

$- 6 x + 4 y = 18$

$3 (2 x) + 3 (- 3 y) = (3) (- 16)$

Multiply.

Multiply $2$ by $3$ .

$- 6 x + 4 y = 18$

$6 x + 3 (- 3 y) = (3) (- 16)$

Multiply $- 3$ by $3$ .

$- 6 x + 4 y = 18$

$6 x - 9 y = (3) (- 16)$

$- 6 x + 4 y = 18$

$6 x - 9 y = (3) (- 16)$

$- 6 x + 4 y = 18$

$6 x - 9 y = (3) (- 16)$

$- 6 x + 4 y = 18$

$6 x - 9 y = (3) (- 16)$

Simplify the right side.

Multiply $3$ by $- 16$ .

$- 6 x + 4 y = 18$

$6 x - 9 y = - 48$

$- 6 x + 4 y = 18$

$6 x - 9 y = - 48$

$- 6 x + 4 y = 18$

$6 x - 9 y = - 48$

Step 3

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

	$-$	$6$	$x$	$+$	$4$	$y$	$=$		$1$	$8$
$+$		$6$	$x$	$-$	$9$	$y$	$=$	$-$	$4$	$8$
				$-$	$5$	$y$	$=$	$-$	$3$	$0$

Step 4

Divide each term in $- 5 y = - 30$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 30$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 30}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 30}{- 5}$

Divide $y$ by $1$ .

$y = \frac{- 30}{- 5}$

Simplify the right side.

Divide $- 30$ by $- 5$ .

$y = 6$

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 $x$ .

$- 6 x + 4 (6) = 18$

Multiply $4$ by $6$ .

$- 6 x + 24 = 18$

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

Subtract $24$ from both sides of the equation.

$- 6 x = 18 - 24$

Subtract $24$ from $18$ .

$- 6 x = - 6$

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

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

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $- 6$ .

$x = 1$

Step 6

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

$(1, 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(1, 6)$

Equation Form:

$x = 1, y = 6$

Step 8

Solve by Addition/Elimination 3x-2y=-9 2x-3y=-16

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