Solve by Addition/Elimination 2x+5y=0 x-5y=-15

$2 x + 5 y = 0$ $x - 5 y = - 15$

Step 1

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

$2 x + 5 y = 0$

$(- 2) \cdot (x - 5 y) = (- 2) (- 15)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (x - 5 y)$ .

Apply the distributive property.

$2 x + 5 y = 0$

$- 2 x - 2 (- 5 y) = (- 2) (- 15)$

Multiply $- 5$ by $- 2$ .

$2 x + 5 y = 0$

$- 2 x + 10 y = (- 2) (- 15)$

$2 x + 5 y = 0$

$- 2 x + 10 y = (- 2) (- 15)$

$2 x + 5 y = 0$

$- 2 x + 10 y = (- 2) (- 15)$

Simplify the right side.

Multiply $- 2$ by $- 15$ .

$2 x + 5 y = 0$

$- 2 x + 10 y = 30$

$2 x + 5 y = 0$

$- 2 x + 10 y = 30$

$2 x + 5 y = 0$

$- 2 x + 10 y = 30$

Step 3

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

		$2$	$x$	$+$		$5$	$y$	$=$		$0$
$+$	$-$	$2$	$x$	$+$	$1$	$0$	$y$	$=$	$3$	$0$
					$1$	$5$	$y$	$=$	$3$	$0$

Step 4

Divide each term in $15 y = 30$ by $15$ and simplify.

Divide each term in $15 y = 30$ by $15$ .

$\frac{15 y}{15} = \frac{30}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{30}{15}$

Divide $y$ by $1$ .

$y = \frac{30}{15}$

Simplify the right side.

Divide $30$ by $15$ .

$y = 2$

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 $x$ .

$2 x + 5 (2) = 0$

Multiply $5$ by $2$ .

$2 x + 10 = 0$

Subtract $10$ from both sides of the equation.

$2 x = - 10$

Divide each term in $2 x = - 10$ by $2$ and simplify.

Divide each term in $2 x = - 10$ by $2$ .

$\frac{2 x}{2} = \frac{- 10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 10}{2}$

Divide $x$ by $1$ .

$x = \frac{- 10}{2}$

Simplify the right side.

Divide $- 10$ by $2$ .

$x = - 5$

Step 6

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

$(- 5, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 5, 2)$

Equation Form:

$x = - 5, y = 2$

Step 8

Solve by Addition/Elimination 2x+5y=0 x-5y=-15

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