Solve by Addition/Elimination -9x+4y=6 9x+5y=-33

$- 9 x + 4 y = 6$ $9 x + 5 y = - 33$

Step 1

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

	$-$	$9$	$x$	$+$	$4$	$y$	$=$			$6$
$+$		$9$	$x$	$+$	$5$	$y$	$=$	$-$	$3$	$3$
					$9$	$y$	$=$	$-$	$2$	$7$

Step 2

Divide each term in $9 y = - 27$ by $9$ and simplify.

Divide each term in $9 y = - 27$ by $9$ .

$\frac{9 y}{9} = \frac{- 27}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 27}{9}$

Divide $y$ by $1$ .

$y = \frac{- 27}{9}$

Simplify the right side.

Divide $- 27$ by $9$ .

$y = - 3$

Step 3

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 $x$ .

$- 9 x + 4 (- 3) = 6$

Multiply $4$ by $- 3$ .

$- 9 x - 12 = 6$

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

Add $12$ to both sides of the equation.

$- 9 x = 6 + 12$

Add $6$ and $12$ .

$- 9 x = 18$

Divide each term in $- 9 x = 18$ by $- 9$ and simplify.

Divide each term in $- 9 x = 18$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{18}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{18}{- 9}$

Divide $x$ by $1$ .

$x = \frac{18}{- 9}$

Simplify the right side.

Divide $18$ by $- 9$ .

$x = - 2$

Step 4

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

$(- 2, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, - 3)$

Equation Form:

$x = - 2, y = - 3$

Step 6

Solve by Addition/Elimination -9x+4y=6 9x+5y=-33

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