Solve by Addition/Elimination 2x-12=-4y , 7x+6y=-14

$2 x - 12 = - 4 y$ , $7 x + 6 y = - 14$

Step 1

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

Add $4 y$ to both sides of the equation.

$2 x - 12 + 4 y = 0$

$7 x + 6 y = - 14$

Move $- 12$ .

$2 x + 4 y - 12 = 0$

$7 x + 6 y = - 14$

$2 x + 4 y - 12 = 0$

$7 x + 6 y = - 14$

Step 2

Add $12$ to both sides of the equation.

$2 x + 4 y = 12$

$7 x + 6 y = - 14$

Step 3

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

$(- 3) \cdot (2 x + 4 y) = (- 3) (12)$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 3) \cdot (2 x + 4 y)$ .

Apply the distributive property.

$- 3 (2 x) - 3 (4 y) = (- 3) (12)$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

Multiply.

Multiply $2$ by $- 3$ .

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

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

Multiply $4$ by $- 3$ .

$- 6 x - 12 y = (- 3) (12)$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

$- 6 x - 12 y = (- 3) (12)$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

$- 6 x - 12 y = (- 3) (12)$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

$- 6 x - 12 y = (- 3) (12)$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

Simplify the right side.

Multiply $- 3$ by $12$ .

$- 6 x - 12 y = - 36$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

$- 6 x - 12 y = - 36$

$(2) \cdot (7 x + 6 y) = (2) (- 14)$

Simplify the left side.

Simplify $(2) \cdot (7 x + 6 y)$ .

Apply the distributive property.

$- 6 x - 12 y = - 36$

$2 (7 x) + 2 (6 y) = (2) (- 14)$

Multiply.

Multiply $7$ by $2$ .

$- 6 x - 12 y = - 36$

$14 x + 2 (6 y) = (2) (- 14)$

Multiply $6$ by $2$ .

$- 6 x - 12 y = - 36$

$14 x + 12 y = (2) (- 14)$

$- 6 x - 12 y = - 36$

$14 x + 12 y = (2) (- 14)$

$- 6 x - 12 y = - 36$

$14 x + 12 y = (2) (- 14)$

$- 6 x - 12 y = - 36$

$14 x + 12 y = (2) (- 14)$

Simplify the right side.

Multiply $2$ by $- 14$ .

$- 6 x - 12 y = - 36$

$14 x + 12 y = - 28$

$- 6 x - 12 y = - 36$

$14 x + 12 y = - 28$

$- 6 x - 12 y = - 36$

$14 x + 12 y = - 28$

Step 5

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

	$-$	$6$	$x$	$-$	$1$	$2$	$y$	$=$	$-$	$3$	$6$
$+$	$1$	$4$	$x$	$+$	$1$	$2$	$y$	$=$	$-$	$2$	$8$
		$8$	$x$					$=$	$-$	$6$	$4$

Step 6

Divide each term in $8 x = - 64$ by $8$ and simplify.

Divide each term in $8 x = - 64$ by $8$ .

$\frac{8 x}{8} = \frac{- 64}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 64}{8}$

Divide $x$ by $1$ .

$x = \frac{- 64}{8}$

Simplify the right side.

Divide $- 64$ by $8$ .

$x = - 8$

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 $y$ .

$- 6 \cdot - 8 - 12 y = - 36$

Multiply $- 6$ by $- 8$ .

$48 - 12 y = - 36$

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

Subtract $48$ from both sides of the equation.

$- 12 y = - 36 - 48$

Subtract $48$ from $- 36$ .

$- 12 y = - 84$

Divide each term in $- 12 y = - 84$ by $- 12$ and simplify.

Divide each term in $- 12 y = - 84$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{- 84}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{- 84}{- 12}$

Divide $y$ by $1$ .

$y = \frac{- 84}{- 12}$

Simplify the right side.

Divide $- 84$ by $- 12$ .

$y = 7$

Step 8

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

$(- 8, 7)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 8, 7)$

Equation Form:

$x = - 8, y = 7$

Step 10

Solve by Addition/Elimination 2x-12=-4y , 7x+6y=-14

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