Solve by Addition/Elimination -x-7y=14 , -4x-14y=28

$- x - 7 y = 14$ , $- 4 x - 14 y = 28$

Step 1

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

$(- 4) \cdot (- x - 7 y) = (- 4) (14)$

$- 4 x - 14 y = 28$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (- x - 7 y)$ .

Apply the distributive property.

$- 4 (- x) - 4 (- 7 y) = (- 4) (14)$

$- 4 x - 14 y = 28$

Multiply.

Multiply $- 1$ by $- 4$ .

$4 x - 4 (- 7 y) = (- 4) (14)$

$- 4 x - 14 y = 28$

Multiply $- 7$ by $- 4$ .

$4 x + 28 y = (- 4) (14)$

$- 4 x - 14 y = 28$

$4 x + 28 y = (- 4) (14)$

$- 4 x - 14 y = 28$

$4 x + 28 y = (- 4) (14)$

$- 4 x - 14 y = 28$

$4 x + 28 y = (- 4) (14)$

$- 4 x - 14 y = 28$

Simplify the right side.

Multiply $- 4$ by $14$ .

$4 x + 28 y = - 56$

$- 4 x - 14 y = 28$

$4 x + 28 y = - 56$

$- 4 x - 14 y = 28$

$4 x + 28 y = - 56$

$- 4 x - 14 y = 28$

Step 3

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

		$4$	$x$	$+$	$2$	$8$	$y$	$=$	$-$	$5$	$6$
$+$	$-$	$4$	$x$	$-$	$1$	$4$	$y$	$=$		$2$	$8$
					$1$	$4$	$y$	$=$	$-$	$2$	$8$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 28$ by $14$ .

$y = - 2$

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 $x$ .

$4 x + 28 (- 2) = - 56$

Multiply $28$ by $- 2$ .

$4 x - 56 = - 56$

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

Add $56$ to both sides of the equation.

$4 x = - 56 + 56$

Add $- 56$ and $56$ .

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

Step 6

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

$(0, - 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(0, - 2)$

Equation Form:

$x = 0, y = - 2$

Step 8

Solve by Addition/Elimination -x-7y=14 , -4x-14y=28

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