Solve by Addition/Elimination 4x+8y=16 3x+6y=12

$4 x + 8 y = 16$ $3 x + 6 y = 12$

Step 1

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

$(- 3) \cdot (4 x + 8 y) = (- 3) (16)$

$(4) \cdot (3 x + 6 y) = (4) (12)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (4 x + 8 y)$ .

Apply the distributive property.

$- 3 (4 x) - 3 (8 y) = (- 3) (16)$

$(4) \cdot (3 x + 6 y) = (4) (12)$

Multiply.

Multiply $4$ by $- 3$ .

$- 12 x - 3 (8 y) = (- 3) (16)$

$(4) \cdot (3 x + 6 y) = (4) (12)$

Multiply $8$ by $- 3$ .

$- 12 x - 24 y = (- 3) (16)$

$(4) \cdot (3 x + 6 y) = (4) (12)$

$- 12 x - 24 y = (- 3) (16)$

$(4) \cdot (3 x + 6 y) = (4) (12)$

$- 12 x - 24 y = (- 3) (16)$

$(4) \cdot (3 x + 6 y) = (4) (12)$

$- 12 x - 24 y = (- 3) (16)$

$(4) \cdot (3 x + 6 y) = (4) (12)$

Simplify the right side.

Multiply $- 3$ by $16$ .

$- 12 x - 24 y = - 48$

$(4) \cdot (3 x + 6 y) = (4) (12)$

$- 12 x - 24 y = - 48$

$(4) \cdot (3 x + 6 y) = (4) (12)$

Simplify the left side.

Simplify $(4) \cdot (3 x + 6 y)$ .

Apply the distributive property.

$- 12 x - 24 y = - 48$

$4 (3 x) + 4 (6 y) = (4) (12)$

Multiply.

Multiply $3$ by $4$ .

$- 12 x - 24 y = - 48$

$12 x + 4 (6 y) = (4) (12)$

Multiply $6$ by $4$ .

$- 12 x - 24 y = - 48$

$12 x + 24 y = (4) (12)$

$- 12 x - 24 y = - 48$

$12 x + 24 y = (4) (12)$

$- 12 x - 24 y = - 48$

$12 x + 24 y = (4) (12)$

$- 12 x - 24 y = - 48$

$12 x + 24 y = (4) (12)$

Simplify the right side.

Multiply $4$ by $12$ .

$- 12 x - 24 y = - 48$

$12 x + 24 y = 48$

$- 12 x - 24 y = - 48$

$12 x + 24 y = 48$

$- 12 x - 24 y = - 48$

$12 x + 24 y = 48$

Step 3

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

	$-$	$1$	$2$	$x$	$-$	$2$	$4$	$y$	$=$	$-$	$4$	$8$
$+$		$1$	$2$	$x$	$+$	$2$	$4$	$y$	$=$		$4$	$8$
								$0$	$=$			$0$

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 $y$ .

Add $12 x$ to both sides of the equation.

$- 24 y = - 48 + 12 x$

Divide each term in $- 24 y = - 48 + 12 x$ by $- 24$ and simplify.

Divide each term in $- 24 y = - 48 + 12 x$ by $- 24$ .

$\frac{- 24 y}{- 24} = \frac{- 48}{- 24} + \frac{12 x}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 y}{- 24} = \frac{- 48}{- 24} + \frac{12 x}{- 24}$

Divide $y$ by $1$ .

$y = \frac{- 48}{- 24} + \frac{12 x}{- 24}$

Simplify the right side.

Simplify each term.

Divide $- 48$ by $- 24$ .

$y = 2 + \frac{12 x}{- 24}$

Cancel the common factor of $12$ and $- 24$ .

Factor $12$ out of $12 x$ .

$y = 2 + \frac{12 (x)}{- 24}$

Cancel the common factors.

Factor $12$ out of $- 24$ .

$y = 2 + \frac{12 x}{12 \cdot - 2}$

Cancel the common factor.

$y = 2 + \frac{12 x}{12 \cdot - 2}$

Rewrite the expression.

$y = 2 + \frac{x}{- 2}$

Move the negative in front of the fraction.

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

Step 6

The solution is the set of ordered pairs that make $y = 2 - \frac{x}{2}$ true.

$(x, 2 - \frac{x}{2})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(x, 2 - \frac{x}{2})$

Equation Form:

$x = x, y = 2 - \frac{x}{2}$

Step 8

Solve by Addition/Elimination 4x+8y=16 3x+6y=12

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