Solve by Addition/Elimination 2x-y=-15 2(x+3y)=-22

$2 x - y = - 15$ $2 (x + 3 y) = - 22$

Step 1

Simplify the left side.

Simplify $2 (x + 3 y)$ .

Apply the distributive property.

$2 x + 2 (3 y) = - 22$

$2 x - y = - 15$

Multiply $3$ by $2$ .

$2 x + 6 y = - 22$

$2 x - y = - 15$

$2 x + 6 y = - 22$

$2 x - y = - 15$

$2 x + 6 y = - 22$

$2 x - y = - 15$

Step 2

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

$(- 1) \cdot (2 x - y) = (- 1) (- 15)$

$2 x + 6 y = - 22$

Step 3

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (2 x - y)$ .

Apply the distributive property.

$- 1 (2 x) - 1 (- y) = (- 1) (- 15)$

$2 x + 6 y = - 22$

Multiply $2$ by $- 1$ .

$- 2 x - 1 (- y) = (- 1) (- 15)$

$2 x + 6 y = - 22$

Multiply $- 1 (- y)$ .

Multiply $- 1$ by $- 1$ .

$- 2 x + 1 y = (- 1) (- 15)$

$2 x + 6 y = - 22$

Multiply $y$ by $1$ .

$- 2 x + y = (- 1) (- 15)$

$2 x + 6 y = - 22$

$- 2 x + y = (- 1) (- 15)$

$2 x + 6 y = - 22$

$- 2 x + y = (- 1) (- 15)$

$2 x + 6 y = - 22$

$- 2 x + y = (- 1) (- 15)$

$2 x + 6 y = - 22$

Simplify the right side.

Multiply $- 1$ by $- 15$ .

$- 2 x + y = 15$

$2 x + 6 y = - 22$

$- 2 x + y = 15$

$2 x + 6 y = - 22$

$- 2 x + y = 15$

$2 x + 6 y = - 22$

Step 4

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

	$-$	$2$	$x$	$+$		$y$	$=$		$1$	$5$
$+$		$2$	$x$	$+$	$6$	$y$	$=$	$-$	$2$	$2$
					$7$	$y$	$=$		$-$	$7$

Step 5

Divide each term in $7 y = - 7$ by $7$ and simplify.

Divide each term in $7 y = - 7$ by $7$ .

$\frac{7 y}{7} = \frac{- 7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 7}{7}$

Divide $y$ by $1$ .

$y = \frac{- 7}{7}$

Simplify the right side.

Divide $- 7$ by $7$ .

$y = - 1$

Step 6

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 $x$ .

$- 2 x - 1 = 15$

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

Add $1$ to both sides of the equation.

$- 2 x = 15 + 1$

Add $15$ and $1$ .

$- 2 x = 16$

Divide each term in $- 2 x = 16$ by $- 2$ and simplify.

Divide each term in $- 2 x = 16$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{16}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{16}{- 2}$

Divide $x$ by $1$ .

$x = \frac{16}{- 2}$

Simplify the right side.

Divide $16$ by $- 2$ .

$x = - 8$

Step 7

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

$(- 8, - 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 8, - 1)$

Equation Form:

$x = - 8, y = - 1$

Step 9

Solve by Addition/Elimination 2x-y=-15 2(x+3y)=-22

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