Solve by Addition/Elimination -5x+2y=6 , 10x-2y=-16

$- 5 x + 2 y = 6$ , $10 x - 2 y = - 16$

Step 1

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

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

Step 2

Divide each term in $5 x = - 10$ by $5$ and simplify.

Divide each term in $5 x = - 10$ by $5$ .

$\frac{5 x}{5} = \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 10}{5}$

Divide $x$ by $1$ .

$x = \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$x = - 2$

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 $y$ .

$- 5 \cdot - 2 + 2 y = 6$

Multiply $- 5$ by $- 2$ .

$10 + 2 y = 6$

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

Subtract $10$ from both sides of the equation.

$2 y = 6 - 10$

Subtract $10$ from $6$ .

$2 y = - 4$

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.

$(- 2, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, - 2)$

Equation Form:

$x = - 2, y = - 2$

Step 6

Solve by Addition/Elimination -5x+2y=6 , 10x-2y=-16

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