Solve by Addition/Elimination 4x+2y=0 x-5y=-11

$4 x + 2 y = 0$ $x - 5 y = - 11$

Step 1

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

$4 x + 2 y = 0$

$(- 4) \cdot (x - 5 y) = (- 4) (- 11)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 4) \cdot (x - 5 y)$ .

Apply the distributive property.

$4 x + 2 y = 0$

$- 4 x - 4 (- 5 y) = (- 4) (- 11)$

Multiply $- 5$ by $- 4$ .

$4 x + 2 y = 0$

$- 4 x + 20 y = (- 4) (- 11)$

$4 x + 2 y = 0$

$- 4 x + 20 y = (- 4) (- 11)$

$4 x + 2 y = 0$

$- 4 x + 20 y = (- 4) (- 11)$

Simplify the right side.

Multiply $- 4$ by $- 11$ .

$4 x + 2 y = 0$

$- 4 x + 20 y = 44$

$4 x + 2 y = 0$

$- 4 x + 20 y = 44$

$4 x + 2 y = 0$

$- 4 x + 20 y = 44$

Step 3

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

		$4$	$x$	$+$		$2$	$y$	$=$		$0$
$+$	$-$	$4$	$x$	$+$	$2$	$0$	$y$	$=$	$4$	$4$
					$2$	$2$	$y$	$=$	$4$	$4$

Step 4

Divide each term in $22 y = 44$ by $22$ and simplify.

Divide each term in $22 y = 44$ by $22$ .

$\frac{22 y}{22} = \frac{44}{22}$

Simplify the left side.

Cancel the common factor of $22$ .

Cancel the common factor.

$\frac{22 y}{22} = \frac{44}{22}$

Divide $y$ by $1$ .

$y = \frac{44}{22}$

Simplify the right side.

Divide $44$ by $22$ .

$y = 2$

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 $x$ .

$4 x + 2 (2) = 0$

Multiply $2$ by $2$ .

$4 x + 4 = 0$

Subtract $4$ from both sides of the equation.

$4 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $4$ .

$x = - 1$

Step 6

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

$(- 1, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 1, 2)$

Equation Form:

$x = - 1, y = 2$

Step 8

Solve by Addition/Elimination 4x+2y=0 x-5y=-11

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