Solve by Addition/Elimination 4x+6y=-42 , 2x-4y=0

$4 x + 6 y = - 42$ , $2 x - 4 y = 0$

Step 1

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

$4 x + 6 y = - 42$

$(- 2) \cdot (2 x - 4 y) = (- 2) (0)$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$4 x + 6 y = - 42$

$- 2 (2 x) - 2 (- 4 y) = (- 2) (0)$

Multiply.

Multiply $2$ by $- 2$ .

$4 x + 6 y = - 42$

$- 4 x - 2 (- 4 y) = (- 2) (0)$

Multiply $- 4$ by $- 2$ .

$4 x + 6 y = - 42$

$- 4 x + 8 y = (- 2) (0)$

$4 x + 6 y = - 42$

$- 4 x + 8 y = (- 2) (0)$

$4 x + 6 y = - 42$

$- 4 x + 8 y = (- 2) (0)$

$4 x + 6 y = - 42$

$- 4 x + 8 y = (- 2) (0)$

Simplify the right side.

Multiply $- 2$ by $0$ .

$4 x + 6 y = - 42$

$- 4 x + 8 y = 0$

$4 x + 6 y = - 42$

$- 4 x + 8 y = 0$

$4 x + 6 y = - 42$

$- 4 x + 8 y = 0$

Step 3

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

		$4$	$x$	$+$	$6$	$y$	$=$	$-$	$4$	$2$
$+$	$-$	$4$	$x$	$+$	$8$	$y$	$=$			$0$
				$1$	$4$	$y$	$=$	$-$	$4$	$2$

Step 4

Divide each term in $14 y = - 42$ by $14$ and simplify.

Divide each term in $14 y = - 42$ by $14$ .

$\frac{14 y}{14} = \frac{- 42}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 y}{14} = \frac{- 42}{14}$

Divide $y$ by $1$ .

$y = \frac{- 42}{14}$

Simplify the right side.

Divide $- 42$ by $14$ .

$y = - 3$

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 $x$ .

$4 x + 6 (- 3) = - 42$

Multiply $6$ by $- 3$ .

$4 x - 18 = - 42$

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

Add $18$ to both sides of the equation.

$4 x = - 42 + 18$

Add $- 42$ and $18$ .

$4 x = - 24$

Divide each term in $4 x = - 24$ by $4$ and simplify.

Divide each term in $4 x = - 24$ by $4$ .

$\frac{4 x}{4} = \frac{- 24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 24}{4}$

Divide $x$ by $1$ .

$x = \frac{- 24}{4}$

Simplify the right side.

Divide $- 24$ by $4$ .

$x = - 6$

Step 6

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

$(- 6, - 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 6, - 3)$

Equation Form:

$x = - 6, y = - 3$

Step 8

Solve by Addition/Elimination 4x+6y=-42 , 2x-4y=0

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