Solve by Addition/Elimination 2x-3y=9 -5x-3y=30

$2 x - 3 y = 9$ $- 5 x - 3 y = 30$

Step 1

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

$(- 1) \cdot (2 x - 3 y) = (- 1) (9)$

$- 5 x - 3 y = 30$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (2 x - 3 y)$ .

Apply the distributive property.

$- 1 (2 x) - 1 (- 3 y) = (- 1) (9)$

$- 5 x - 3 y = 30$

Multiply.

Multiply $2$ by $- 1$ .

$- 2 x - 1 (- 3 y) = (- 1) (9)$

$- 5 x - 3 y = 30$

Multiply $- 3$ by $- 1$ .

$- 2 x + 3 y = (- 1) (9)$

$- 5 x - 3 y = 30$

$- 2 x + 3 y = (- 1) (9)$

$- 5 x - 3 y = 30$

$- 2 x + 3 y = (- 1) (9)$

$- 5 x - 3 y = 30$

$- 2 x + 3 y = (- 1) (9)$

$- 5 x - 3 y = 30$

Simplify the right side.

Multiply $- 1$ by $9$ .

$- 2 x + 3 y = - 9$

$- 5 x - 3 y = 30$

$- 2 x + 3 y = - 9$

$- 5 x - 3 y = 30$

$- 2 x + 3 y = - 9$

$- 5 x - 3 y = 30$

Step 3

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

	$-$	$2$	$x$	$+$	$3$	$y$	$=$	$-$	$9$
$+$	$-$	$5$	$x$	$-$	$3$	$y$	$=$	$3$	$0$
	$-$	$7$	$x$				$=$	$2$	$1$

Step 4

Divide each term in $- 7 x = 21$ by $- 7$ and simplify.

Divide each term in $- 7 x = 21$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{21}{- 7}$

Divide $x$ by $1$ .

$x = \frac{21}{- 7}$

Simplify the right side.

Divide $21$ by $- 7$ .

$x = - 3$

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 $y$ .

$- 2 \cdot - 3 + 3 y = - 9$

Multiply $- 2$ by $- 3$ .

$6 + 3 y = - 9$

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

Subtract $6$ from both sides of the equation.

$3 y = - 9 - 6$

Subtract $6$ from $- 9$ .

$3 y = - 15$

Divide each term in $3 y = - 15$ by $3$ and simplify.

Divide each term in $3 y = - 15$ by $3$ .

$\frac{3 y}{3} = \frac{- 15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 15}{3}$

Divide $y$ by $1$ .

$y = \frac{- 15}{3}$

Simplify the right side.

Divide $- 15$ by $3$ .

$y = - 5$

Step 6

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

$(- 3, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 3, - 5)$

Equation Form:

$x = - 3, y = - 5$

Step 8

Solve by Addition/Elimination 2x-3y=9 -5x-3y=30

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