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

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

Step 1

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

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

$2 x - 3 y = 9$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

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

$2 x - 3 y = 9$

Multiply $- 2$ by $- 2$ .

$- 2 x + 4 y = (- 2) (3)$

$2 x - 3 y = 9$

$- 2 x + 4 y = (- 2) (3)$

$2 x - 3 y = 9$

$- 2 x + 4 y = (- 2) (3)$

$2 x - 3 y = 9$

Simplify the right side.

Multiply $- 2$ by $3$ .

$- 2 x + 4 y = - 6$

$2 x - 3 y = 9$

$- 2 x + 4 y = - 6$

$2 x - 3 y = 9$

$- 2 x + 4 y = - 6$

$2 x - 3 y = 9$

Step 3

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

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

Step 4

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 $x$ .

$- 2 x + 4 (3) = - 6$

Multiply $4$ by $3$ .

$- 2 x + 12 = - 6$

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

Subtract $12$ from both sides of the equation.

$- 2 x = - 6 - 12$

Subtract $12$ from $- 6$ .

$- 2 x = - 18$

Divide each term in $- 2 x = - 18$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 18$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 18}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 18}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 2}$

Simplify the right side.

Divide $- 18$ by $- 2$ .

$x = 9$

Step 5

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

$(9, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, 3)$

Equation Form:

$x = 9, y = 3$

Step 7

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

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