Solve by Addition/Elimination x-3y=-6 2x-7y=10

$x - 3 y = - 6$ $2 x - 7 y = 10$

Step 1

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

$(- 2) \cdot (x - 3 y) = (- 2) (- 6)$

$2 x - 7 y = 10$

Step 2

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 x - 2 (- 3 y) = (- 2) (- 6)$

$2 x - 7 y = 10$

Multiply $- 3$ by $- 2$ .

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

$2 x - 7 y = 10$

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

$2 x - 7 y = 10$

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

$2 x - 7 y = 10$

Simplify the right side.

Multiply $- 2$ by $- 6$ .

$- 2 x + 6 y = 12$

$2 x - 7 y = 10$

$- 2 x + 6 y = 12$

$2 x - 7 y = 10$

$- 2 x + 6 y = 12$

$2 x - 7 y = 10$

Step 3

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

	$-$	$2$	$x$	$+$	$6$	$y$	$=$	$1$	$2$
$+$		$2$	$x$	$-$	$7$	$y$	$=$	$1$	$0$
					$-$	$y$	$=$	$2$	$2$

Step 4

Divide each term in $- y = 22$ by $- 1$ and simplify.

Divide each term in $- y = 22$ by $- 1$ .

$\frac{- y}{- 1} = \frac{22}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{22}{- 1}$

Divide $y$ by $1$ .

$y = \frac{22}{- 1}$

Simplify the right side.

Divide $22$ by $- 1$ .

$y = - 22$

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 $x$ .

$- 2 x + 6 (- 22) = 12$

Multiply $6$ by $- 22$ .

$- 2 x - 132 = 12$

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

Add $132$ to both sides of the equation.

$- 2 x = 12 + 132$

Add $12$ and $132$ .

$- 2 x = 144$

Divide each term in $- 2 x = 144$ by $- 2$ and simplify.

Divide each term in $- 2 x = 144$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{144}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{144}{- 2}$

Divide $x$ by $1$ .

$x = \frac{144}{- 2}$

Simplify the right side.

Divide $144$ by $- 2$ .

$x = - 72$

Step 6

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

$(- 72, - 22)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 72, - 22)$

Equation Form:

$x = - 72, y = - 22$

Step 8

Solve by Addition/Elimination x-3y=-6 2x-7y=10

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