Solve by Addition/Elimination 3c-8d=7 c+2d=-7

$3 c - 8 d = 7$ $c + 2 d = - 7$

Step 1

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

$3 c - 8 d = 7$

$(- 3) \cdot (c + 2 d) = (- 3) (- 7)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (c + 2 d)$ .

Apply the distributive property.

$3 c - 8 d = 7$

$- 3 c - 3 (2 d) = (- 3) (- 7)$

Multiply $2$ by $- 3$ .

$3 c - 8 d = 7$

$- 3 c - 6 d = (- 3) (- 7)$

$3 c - 8 d = 7$

$- 3 c - 6 d = (- 3) (- 7)$

$3 c - 8 d = 7$

$- 3 c - 6 d = (- 3) (- 7)$

Simplify the right side.

Multiply $- 3$ by $- 7$ .

$3 c - 8 d = 7$

$- 3 c - 6 d = 21$

$3 c - 8 d = 7$

$- 3 c - 6 d = 21$

$3 c - 8 d = 7$

$- 3 c - 6 d = 21$

Step 3

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

		$3$	$c$		$-$	$8$	$d$	$=$		$7$
$+$	$-$	$3$	$c$		$-$	$6$	$d$	$=$	$2$	$1$
				$-$	$1$	$4$	$d$	$=$	$2$	$8$

Step 4

Divide each term in $- 14 d = 28$ by $- 14$ and simplify.

Divide each term in $- 14 d = 28$ by $- 14$ .

$\frac{- 14 d}{- 14} = \frac{28}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 d}{- 14} = \frac{28}{- 14}$

Divide $d$ by $1$ .

$d = \frac{28}{- 14}$

Simplify the right side.

Divide $28$ by $- 14$ .

$d = - 2$

Step 5

Substitute the value found for $d$ into one of the original equations, then solve for $c$ .

Substitute the value found for $d$ into one of the original equations to solve for $c$ .

$3 c - 8 \cdot - 2 = 7$

Multiply $- 8$ by $- 2$ .

$3 c + 16 = 7$

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

Subtract $16$ from both sides of the equation.

$3 c = 7 - 16$

Subtract $16$ from $7$ .

$3 c = - 9$

Divide each term in $3 c = - 9$ by $3$ and simplify.

Divide each term in $3 c = - 9$ by $3$ .

$\frac{3 c}{3} = \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 c}{3} = \frac{- 9}{3}$

Divide $c$ by $1$ .

$c = \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$c = - 3$

Step 6

This is the final solution to the independent system of equations.

$d = - 2$

$c = - 3$

Solve by Addition/Elimination 3c-8d=7 c+2d=-7

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