Solve by Addition/Elimination 12x+3y=0 , -36x-9y=0

$12 x + 3 y = 0$ , $- 36 x - 9 y = 0$

Step 1

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

$(3) \cdot (12 x + 3 y) = (3) (0)$

$- 36 x - 9 y = 0$

Step 2

Simplify.

Simplify the left side.

Simplify $(3) \cdot (12 x + 3 y)$ .

Apply the distributive property.

$3 (12 x) + 3 (3 y) = (3) (0)$

$- 36 x - 9 y = 0$

Multiply.

Multiply $12$ by $3$ .

$36 x + 3 (3 y) = (3) (0)$

$- 36 x - 9 y = 0$

Multiply $3$ by $3$ .

$36 x + 9 y = (3) (0)$

$- 36 x - 9 y = 0$

$36 x + 9 y = (3) (0)$

$- 36 x - 9 y = 0$

$36 x + 9 y = (3) (0)$

$- 36 x - 9 y = 0$

$36 x + 9 y = (3) (0)$

$- 36 x - 9 y = 0$

Simplify the right side.

Multiply $3$ by $0$ .

$36 x + 9 y = 0$

$- 36 x - 9 y = 0$

$36 x + 9 y = 0$

$- 36 x - 9 y = 0$

$36 x + 9 y = 0$

$- 36 x - 9 y = 0$

Step 3

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

		$3$	$6$	$x$	$+$	$9$	$y$	$=$	$0$
$+$	$-$	$3$	$6$	$x$	$-$	$9$	$y$	$=$	$0$
							$0$	$=$	$0$

Step 4

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Step 5

Solve one of the equations for $y$ .

Subtract $36 x$ from both sides of the equation.

$9 y = - 36 x$

Divide each term in $9 y = - 36 x$ by $9$ and simplify.

Divide each term in $9 y = - 36 x$ by $9$ .

$\frac{9 y}{9} = \frac{- 36 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 36 x}{9}$

Divide $y$ by $1$ .

$y = \frac{- 36 x}{9}$

Simplify the right side.

Cancel the common factor of $- 36$ and $9$ .

Factor $9$ out of $- 36 x$ .

$y = \frac{9 (- 4 x)}{9}$

Cancel the common factors.

Factor $9$ out of $9$ .

$y = \frac{9 (- 4 x)}{9 (1)}$

Cancel the common factor.

$y = \frac{9 (- 4 x)}{9 \cdot 1}$

Rewrite the expression.

$y = \frac{- 4 x}{1}$

Divide $- 4 x$ by $1$ .

$y = - 4 x$

Step 6

The solution is the set of ordered pairs that make $y = - 4 x$ true.

$(x, - 4 x)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, - 4 x)$

Equation Form:

$x = x, y = - 4 x$

Step 8

Solve by Addition/Elimination 12x+3y=0 , -36x-9y=0

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