Solve by Addition/Elimination 6x-6=-8y , 7x+6y=-13

$6 x - 6 = - 8 y$ , $7 x + 6 y = - 13$

Step 1

Move all terms containing variables to the left side of the equation.

Add $8 y$ to both sides of the equation.

$6 x - 6 + 8 y = 0$

$7 x + 6 y = - 13$

Move $- 6$ .

$6 x + 8 y - 6 = 0$

$7 x + 6 y = - 13$

$6 x + 8 y - 6 = 0$

$7 x + 6 y = - 13$

Step 2

Add $6$ to both sides of the equation.

$6 x + 8 y = 6$

$7 x + 6 y = - 13$

Step 3

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

$(- 3) \cdot (6 x + 8 y) = (- 3) (6)$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (6 x + 8 y)$ .

Apply the distributive property.

$- 3 (6 x) - 3 (8 y) = (- 3) (6)$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

Multiply.

Multiply $6$ by $- 3$ .

$- 18 x - 3 (8 y) = (- 3) (6)$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

Multiply $8$ by $- 3$ .

$- 18 x - 24 y = (- 3) (6)$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

$- 18 x - 24 y = (- 3) (6)$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

$- 18 x - 24 y = (- 3) (6)$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

$- 18 x - 24 y = (- 3) (6)$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

Simplify the right side.

Multiply $- 3$ by $6$ .

$- 18 x - 24 y = - 18$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

$- 18 x - 24 y = - 18$

$(4) \cdot (7 x + 6 y) = (4) (- 13)$

Simplify the left side.

Simplify $(4) \cdot (7 x + 6 y)$ .

Apply the distributive property.

$- 18 x - 24 y = - 18$

$4 (7 x) + 4 (6 y) = (4) (- 13)$

Multiply.

Multiply $7$ by $4$ .

$- 18 x - 24 y = - 18$

$28 x + 4 (6 y) = (4) (- 13)$

Multiply $6$ by $4$ .

$- 18 x - 24 y = - 18$

$28 x + 24 y = (4) (- 13)$

$- 18 x - 24 y = - 18$

$28 x + 24 y = (4) (- 13)$

$- 18 x - 24 y = - 18$

$28 x + 24 y = (4) (- 13)$

$- 18 x - 24 y = - 18$

$28 x + 24 y = (4) (- 13)$

Simplify the right side.

Multiply $4$ by $- 13$ .

$- 18 x - 24 y = - 18$

$28 x + 24 y = - 52$

$- 18 x - 24 y = - 18$

$28 x + 24 y = - 52$

$- 18 x - 24 y = - 18$

$28 x + 24 y = - 52$

Step 5

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

	$-$	$1$	$8$	$x$	$-$	$2$	$4$	$y$	$=$	$-$	$1$	$8$
$+$		$2$	$8$	$x$	$+$	$2$	$4$	$y$	$=$	$-$	$5$	$2$
		$1$	$0$	$x$					$=$	$-$	$7$	$0$

Step 6

Divide each term in $10 x = - 70$ by $10$ and simplify.

Divide each term in $10 x = - 70$ by $10$ .

$\frac{10 x}{10} = \frac{- 70}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{- 70}{10}$

Divide $x$ by $1$ .

$x = \frac{- 70}{10}$

Simplify the right side.

Divide $- 70$ by $10$ .

$x = - 7$

Step 7

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

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

$- 18 \cdot - 7 - 24 y = - 18$

Multiply $- 18$ by $- 7$ .

$126 - 24 y = - 18$

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

Subtract $126$ from both sides of the equation.

$- 24 y = - 18 - 126$

Subtract $126$ from $- 18$ .

$- 24 y = - 144$

Divide each term in $- 24 y = - 144$ by $- 24$ and simplify.

Divide each term in $- 24 y = - 144$ by $- 24$ .

$\frac{- 24 y}{- 24} = \frac{- 144}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 y}{- 24} = \frac{- 144}{- 24}$

Divide $y$ by $1$ .

$y = \frac{- 144}{- 24}$

Simplify the right side.

Divide $- 144$ by $- 24$ .

$y = 6$

Step 8

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

$(- 7, 6)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 7, 6)$

Equation Form:

$x = - 7, y = 6$

Step 10

Solve by Addition/Elimination 6x-6=-8y , 7x+6y=-13

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