Solve by Addition/Elimination -4x+9y=9 , x-3y=-6

$- 4 x + 9 y = 9$ , $x - 3 y = - 6$

Step 1

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

$- 4 x + 9 y = 9$

$(4) \cdot (x - 3 y) = (4) (- 6)$

Step 2

Simplify.

Simplify the left side.

Simplify $(4) \cdot (x - 3 y)$ .

Apply the distributive property.

$- 4 x + 9 y = 9$

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

Multiply $- 3$ by $4$ .

$- 4 x + 9 y = 9$

$4 x - 12 y = (4) (- 6)$

$- 4 x + 9 y = 9$

$4 x - 12 y = (4) (- 6)$

$- 4 x + 9 y = 9$

$4 x - 12 y = (4) (- 6)$

Simplify the right side.

Multiply $4$ by $- 6$ .

$- 4 x + 9 y = 9$

$4 x - 12 y = - 24$

$- 4 x + 9 y = 9$

$4 x - 12 y = - 24$

$- 4 x + 9 y = 9$

$4 x - 12 y = - 24$

Step 3

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

	$-$	$4$	$x$	$+$		$9$	$y$	$=$			$9$
$+$		$4$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$2$	$4$
					$-$	$3$	$y$	$=$	$-$	$1$	$5$

Step 4

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 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 $x$ .

$- 4 x + 9 (5) = 9$

Multiply $9$ by $5$ .

$- 4 x + 45 = 9$

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

Subtract $45$ from both sides of the equation.

$- 4 x = 9 - 45$

Subtract $45$ from $9$ .

$- 4 x = - 36$

Divide each term in $- 4 x = - 36$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 36$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 36}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 36}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 36}{- 4}$

Simplify the right side.

Divide $- 36$ by $- 4$ .

$x = 9$

Step 6

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

$(9, 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(9, 5)$

Equation Form:

$x = 9, y = 5$

Step 8

Solve by Addition/Elimination -4x+9y=9 , x-3y=-6

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