Solve by Addition/Elimination x-3y=-2 2x-3y=-7

$x - 3 y = - 2$ $2 x - 3 y = - 7$

Step 1

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

$(- 2) \cdot (x - 3 y) = (- 2) (- 2)$

$2 x - 3 y = - 7$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (x - 3 y)$ .

Apply the distributive property.

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

$2 x - 3 y = - 7$

Multiply $- 3$ by $- 2$ .

$- 2 x + 6 y = (- 2) (- 2)$

$2 x - 3 y = - 7$

$- 2 x + 6 y = (- 2) (- 2)$

$2 x - 3 y = - 7$

$- 2 x + 6 y = (- 2) (- 2)$

$2 x - 3 y = - 7$

Simplify the right side.

Multiply $- 2$ by $- 2$ .

$- 2 x + 6 y = 4$

$2 x - 3 y = - 7$

$- 2 x + 6 y = 4$

$2 x - 3 y = - 7$

$- 2 x + 6 y = 4$

$2 x - 3 y = - 7$

Step 3

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

	$-$	$2$	$x$	$+$	$6$	$y$	$=$		$4$
$+$		$2$	$x$	$-$	$3$	$y$	$=$	$-$	$7$
					$3$	$y$	$=$	$-$	$3$

Step 4

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

Divide each term in $3 y = - 3$ by $3$ .

$\frac{3 y}{3} = \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 3}{3}$

Divide $y$ by $1$ .

$y = \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$y = - 1$

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 $x$ .

$- 2 x + 6 (- 1) = 4$

Multiply $6$ by $- 1$ .

$- 2 x - 6 = 4$

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

Add $6$ to both sides of the equation.

$- 2 x = 4 + 6$

Add $4$ and $6$ .

$- 2 x = 10$

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.

$(- 5, - 1)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 5, - 1)$

Equation Form:

$x = - 5, y = - 1$

Step 8

Solve by Addition/Elimination x-3y=-2 2x-3y=-7

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