Solve by Addition/Elimination 6x+7y=96 6x-7y=12

$6 x + 7 y = 96$ $6 x - 7 y = 12$

Step 1

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

$(- 1) \cdot (6 x + 7 y) = (- 1) (96)$

$6 x - 7 y = 12$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (6 x + 7 y)$ .

Apply the distributive property.

$- 1 (6 x) - 1 (7 y) = (- 1) (96)$

$6 x - 7 y = 12$

Multiply.

Multiply $6$ by $- 1$ .

$- 6 x - 1 (7 y) = (- 1) (96)$

$6 x - 7 y = 12$

Multiply $7$ by $- 1$ .

$- 6 x - 7 y = (- 1) (96)$

$6 x - 7 y = 12$

$- 6 x - 7 y = (- 1) (96)$

$6 x - 7 y = 12$

$- 6 x - 7 y = (- 1) (96)$

$6 x - 7 y = 12$

$- 6 x - 7 y = (- 1) (96)$

$6 x - 7 y = 12$

Simplify the right side.

Multiply $- 1$ by $96$ .

$- 6 x - 7 y = - 96$

$6 x - 7 y = 12$

$- 6 x - 7 y = - 96$

$6 x - 7 y = 12$

$- 6 x - 7 y = - 96$

$6 x - 7 y = 12$

Step 3

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

	$-$	$6$	$x$		$-$	$7$	$y$	$=$	$-$	$9$	$6$
$+$		$6$	$x$		$-$	$7$	$y$	$=$		$1$	$2$
				$-$	$1$	$4$	$y$	$=$	$-$	$8$	$4$

Step 4

Divide each term in $- 14 y = - 84$ by $- 14$ and simplify.

Divide each term in $- 14 y = - 84$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{- 84}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{- 84}{- 14}$

Divide $y$ by $1$ .

$y = \frac{- 84}{- 14}$

Simplify the right side.

Divide $- 84$ by $- 14$ .

$y = 6$

Step 5

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$- 6 x - 7 \cdot 6 = - 96$

Multiply $- 7$ by $6$ .

$- 6 x - 42 = - 96$

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

Add $42$ to both sides of the equation.

$- 6 x = - 96 + 42$

Add $- 96$ and $42$ .

$- 6 x = - 54$

Divide each term in $- 6 x = - 54$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 54$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 54}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 54}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 54}{- 6}$

Simplify the right side.

Divide $- 54$ by $- 6$ .

$x = 9$

Step 6

The solution to the independent system of equations can be represented as a point.

$(9, 6)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(9, 6)$

Equation Form:

$x = 9, y = 6$

Step 8

Solve by Addition/Elimination 6x+7y=96 6x-7y=12

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