Solve by Addition/Elimination 2x+3y=18 3x-3y=12

$2 x + 3 y = 18$ $3 x - 3 y = 12$

Step 1

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

	$2$	$x$	$+$	$3$	$y$	$=$	$1$	$8$
$+$	$3$	$x$	$-$	$3$	$y$	$=$	$1$	$2$
	$5$	$x$				$=$	$3$	$0$

Step 2

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

Divide each term in $5 x = 30$ by $5$ .

$\frac{5 x}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{30}{5}$

Divide $x$ by $1$ .

$x = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$

Step 3

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 $y$ .

$2 (6) + 3 y = 18$

Multiply $2$ by $6$ .

$12 + 3 y = 18$

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

Subtract $12$ from both sides of the equation.

$3 y = 18 - 12$

Subtract $12$ from $18$ .

$3 y = 6$

Divide each term in $3 y = 6$ by $3$ and simplify.

Divide each term in $3 y = 6$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3}$

Divide $y$ by $1$ .

$y = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$y = 2$

Step 4

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

$(6, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(6, 2)$

Equation Form:

$x = 6, y = 2$

Step 6

Solve by Addition/Elimination 2x+3y=18 3x-3y=12

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