Solve by Addition/Elimination 12x+4y=0 , -48x-16y=0

$12 x + 4 y = 0$ , $- 48 x - 16 y = 0$

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

$(4) \cdot (12 x + 4 y) = (4) (0)$

$- 48 x - 16 y = 0$

Simplify.

Simplify the left side.

Simplify $(4) \cdot (12 x + 4 y)$ .

Apply the distributive property.

$4 (12 x) + 4 (4 y) = (4) (0)$

$- 48 x - 16 y = 0$

Multiply.

Multiply $12$ by $4$ .

$48 x + 4 (4 y) = (4) (0)$

$- 48 x - 16 y = 0$

Multiply $4$ by $4$ .

$48 x + 16 y = (4) (0)$

$- 48 x - 16 y = 0$

$48 x + 16 y = (4) (0)$

$- 48 x - 16 y = 0$

$48 x + 16 y = (4) (0)$

$- 48 x - 16 y = 0$

$48 x + 16 y = (4) (0)$

$- 48 x - 16 y = 0$

Simplify the right side.

Multiply $4$ by $0$ .

$48 x + 16 y = 0$

$- 48 x - 16 y = 0$

$48 x + 16 y = 0$

$- 48 x - 16 y = 0$

$48 x + 16 y = 0$

$- 48 x - 16 y = 0$

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

		$4$	$8$	$x$	$+$	$1$	$6$	$y$	$=$	$0$
$+$	$-$	$4$	$8$	$x$	$-$	$1$	$6$	$y$	$=$	$0$
								$0$	$=$	$0$

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

Infinite number of solutions

Solve one of the equations for $y$ .

Subtract $48 x$ from both sides of the equation.

$16 y = - 48 x$

Divide each term in $16 y = - 48 x$ by $16$ and simplify.

Divide each term in $16 y = - 48 x$ by $16$ .

$\frac{16 y}{16} = \frac{- 48 x}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 y}{16} = \frac{- 48 x}{16}$

Divide $y$ by $1$ .

$y = \frac{- 48 x}{16}$

Simplify the right side.

Cancel the common factor of $- 48$ and $16$ .

Factor $16$ out of $- 48 x$ .

$y = \frac{16 (- 3 x)}{16}$

Cancel the common factors.

Factor $16$ out of $16$ .

$y = \frac{16 (- 3 x)}{16 (1)}$

Cancel the common factor.

$y = \frac{16 (- 3 x)}{16 \cdot 1}$

Rewrite the expression.

$y = \frac{- 3 x}{1}$

Divide $- 3 x$ by $1$ .

$y = - 3 x$

The solution is the set of ordered pairs that make $y = - 3 x$ true.

$(x, - 3 x)$

The result can be shown in multiple forms.

Point Form:

$(x, - 3 x)$

Equation Form:

$x = x, y = - 3 x$

Solve by Addition/Elimination 12x+4y=0 , -48x-16y=0

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