Solve by Addition/Elimination 3x+6y=36 3x-6y=0

$3 x + 6 y = 36$ $3 x - 6 y = 0$

Step 1

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

$(- 1) \cdot (3 x + 6 y) = (- 1) (36)$

$3 x - 6 y = 0$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (3 x + 6 y)$ .

Apply the distributive property.

$- 1 (3 x) - 1 (6 y) = (- 1) (36)$

$3 x - 6 y = 0$

Multiply.

Multiply $3$ by $- 1$ .

$- 3 x - 1 (6 y) = (- 1) (36)$

$3 x - 6 y = 0$

Multiply $6$ by $- 1$ .

$- 3 x - 6 y = (- 1) (36)$

$3 x - 6 y = 0$

$- 3 x - 6 y = (- 1) (36)$

$3 x - 6 y = 0$

$- 3 x - 6 y = (- 1) (36)$

$3 x - 6 y = 0$

$- 3 x - 6 y = (- 1) (36)$

$3 x - 6 y = 0$

Simplify the right side.

Multiply $- 1$ by $36$ .

$- 3 x - 6 y = - 36$

$3 x - 6 y = 0$

$- 3 x - 6 y = - 36$

$3 x - 6 y = 0$

$- 3 x - 6 y = - 36$

$3 x - 6 y = 0$

Step 3

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

	$-$	$3$	$x$		$-$	$6$	$y$	$=$	$-$	$3$	$6$
$+$		$3$	$x$		$-$	$6$	$y$	$=$			$0$
				$-$	$1$	$2$	$y$	$=$	$-$	$3$	$6$

Step 4

Divide each term in $- 12 y = - 36$ by $- 12$ and simplify.

Divide each term in $- 12 y = - 36$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{- 36}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{- 36}{- 12}$

Divide $y$ by $1$ .

$y = \frac{- 36}{- 12}$

Simplify the right side.

Divide $- 36$ by $- 12$ .

$y = 3$

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 $x$ .

$- 3 x - 6 \cdot 3 = - 36$

Multiply $- 6$ by $3$ .

$- 3 x - 18 = - 36$

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

Add $18$ to both sides of the equation.

$- 3 x = - 36 + 18$

Add $- 36$ and $18$ .

$- 3 x = - 18$

Divide each term in $- 3 x = - 18$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 18$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 18}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 3}$

Simplify the right side.

Divide $- 18$ by $- 3$ .

$x = 6$

Step 6

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

$(6, 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(6, 3)$

Equation Form:

$x = 6, y = 3$

Step 8

Solve by Addition/Elimination 3x+6y=36 3x-6y=0

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