Solve by Addition/Elimination 6w-8z=16 3w-4z=8

$6 w - 8 z = 16$ $3 w - 4 z = 8$

Step 1

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

$6 w - 8 z = 16$

$(- 2) \cdot (3 w - 4 z) = (- 2) (8)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (3 w - 4 z)$ .

Apply the distributive property.

$6 w - 8 z = 16$

$- 2 (3 w) - 2 (- 4 z) = (- 2) (8)$

Multiply.

Multiply $3$ by $- 2$ .

$6 w - 8 z = 16$

$- 6 w - 2 (- 4 z) = (- 2) (8)$

Multiply $- 4$ by $- 2$ .

$6 w - 8 z = 16$

$- 6 w + 8 z = (- 2) (8)$

$6 w - 8 z = 16$

$- 6 w + 8 z = (- 2) (8)$

$6 w - 8 z = 16$

$- 6 w + 8 z = (- 2) (8)$

$6 w - 8 z = 16$

$- 6 w + 8 z = (- 2) (8)$

Simplify the right side.

Multiply $- 2$ by $8$ .

$6 w - 8 z = 16$

$- 6 w + 8 z = - 16$

$6 w - 8 z = 16$

$- 6 w + 8 z = - 16$

$6 w - 8 z = 16$

$- 6 w + 8 z = - 16$

Step 3

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

		$6$	$w$	$-$	$8$	$z$	$=$		$1$	$6$
$+$	$-$	$6$	$w$	$+$	$8$	$z$	$=$	$-$	$1$	$6$
						$0$	$=$			$0$

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 $z$ .

Subtract $6 w$ from both sides of the equation.

$- 8 z = 16 - 6 w$

Divide each term in $- 8 z = 16 - 6 w$ by $- 8$ and simplify.

Divide each term in $- 8 z = 16 - 6 w$ by $- 8$ .

$\frac{- 8 z}{- 8} = \frac{16}{- 8} + \frac{- 6 w}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 z}{- 8} = \frac{16}{- 8} + \frac{- 6 w}{- 8}$

Divide $z$ by $1$ .

$z = \frac{16}{- 8} + \frac{- 6 w}{- 8}$

Simplify the right side.

Simplify each term.

Divide $16$ by $- 8$ .

$z = - 2 + \frac{- 6 w}{- 8}$

Cancel the common factor of $- 6$ and $- 8$ .

Factor $- 2$ out of $- 6 w$ .

$z = - 2 + \frac{- 2 (3 w)}{- 8}$

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

$z = - 2 + \frac{- 2 (3 w)}{- 2 (4)}$

Cancel the common factor.

$z = - 2 + \frac{- 2 (3 w)}{- 2 \cdot 4}$

Rewrite the expression.

$z = - 2 + \frac{3 w}{4}$

Step 6

The solution is the set of ordered pairs that make $z = - 2 + \frac{3 w}{4}$ true.

$(- 2 + \frac{3 w}{4}, w)$

Solve by Addition/Elimination 6w-8z=16 3w-4z=8

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