Solve by Addition/Elimination -3x+2y=8 , 6x-2y=-20

$- 3 x + 2 y = 8$ , $6 x - 2 y = - 20$

Step 1

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

	$-$	$3$	$x$	$+$	$2$	$y$	$=$			$8$
$+$		$6$	$x$	$-$	$2$	$y$	$=$	$-$	$2$	$0$
		$3$	$x$				$=$	$-$	$1$	$2$

Step 2

Divide each term in $3 x = - 12$ by $3$ and simplify.

Divide each term in $3 x = - 12$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 12}{3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$x = - 4$

Step 3

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 $y$ .

$- 3 \cdot - 4 + 2 y = 8$

Multiply $- 3$ by $- 4$ .

$12 + 2 y = 8$

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

Subtract $12$ from both sides of the equation.

$2 y = 8 - 12$

Subtract $12$ from $8$ .

$2 y = - 4$

Divide each term in $2 y = - 4$ by $2$ and simplify.

Divide each term in $2 y = - 4$ by $2$ .

$\frac{2 y}{2} = \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 4}{2}$

Divide $y$ by $1$ .

$y = \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$y = - 2$

Step 4

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

$(- 4, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 4, - 2)$

Equation Form:

$x = - 4, y = - 2$

Step 6

Solve by Addition/Elimination -3x+2y=8 , 6x-2y=-20

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