Solve by Addition/Elimination 6x+5y=-10 3x+5y=20

$6 x + 5 y = - 10$ $3 x + 5 y = 20$

Step 1

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

$(- 1) \cdot (6 x + 5 y) = (- 1) (- 10)$

$3 x + 5 y = 20$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (6 x + 5 y)$ .

Apply the distributive property.

$- 1 (6 x) - 1 (5 y) = (- 1) (- 10)$

$3 x + 5 y = 20$

Multiply.

Multiply $6$ by $- 1$ .

$- 6 x - 1 (5 y) = (- 1) (- 10)$

$3 x + 5 y = 20$

Multiply $5$ by $- 1$ .

$- 6 x - 5 y = (- 1) (- 10)$

$3 x + 5 y = 20$

$- 6 x - 5 y = (- 1) (- 10)$

$3 x + 5 y = 20$

$- 6 x - 5 y = (- 1) (- 10)$

$3 x + 5 y = 20$

$- 6 x - 5 y = (- 1) (- 10)$

$3 x + 5 y = 20$

Simplify the right side.

Multiply $- 1$ by $- 10$ .

$- 6 x - 5 y = 10$

$3 x + 5 y = 20$

$- 6 x - 5 y = 10$

$3 x + 5 y = 20$

$- 6 x - 5 y = 10$

$3 x + 5 y = 20$

Step 3

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

	$-$	$6$	$x$	$-$	$5$	$y$	$=$	$1$	$0$
$+$		$3$	$x$	$+$	$5$	$y$	$=$	$2$	$0$
	$-$	$3$	$x$				$=$	$3$	$0$

Step 4

Divide each term in $- 3 x = 30$ by $- 3$ and simplify.

Divide each term in $- 3 x = 30$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{30}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{30}{- 3}$

Divide $x$ by $1$ .

$x = \frac{30}{- 3}$

Simplify the right side.

Divide $30$ by $- 3$ .

$x = - 10$

Step 5

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 $y$ .

$- 6 \cdot - 10 - 5 y = 10$

Multiply $- 6$ by $- 10$ .

$60 - 5 y = 10$

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

Subtract $60$ from both sides of the equation.

$- 5 y = 10 - 60$

Subtract $60$ from $10$ .

$- 5 y = - 50$

Divide each term in $- 5 y = - 50$ by $- 5$ and simplify.

Divide each term in $- 5 y = - 50$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 50}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 50}{- 5}$

Divide $y$ by $1$ .

$y = \frac{- 50}{- 5}$

Simplify the right side.

Divide $- 50$ by $- 5$ .

$y = 10$

Step 6

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

$(- 10, 10)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 10, 10)$

Equation Form:

$x = - 10, y = 10$

Step 8

Solve by Addition/Elimination 6x+5y=-10 3x+5y=20

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