Determine if Dependent, Independent, or Inconsistent 2x+y=-2 , x+2y=2

$2 x + y = - 2$ , $x + 2 y = 2$

Solve the system of equations.

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

$2 x + y = - 2$

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

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 x + y = - 2$

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

Multiply $2$ by $- 2$ .

$2 x + y = - 2$

$- 2 x - 4 y = (- 2) (2)$

$2 x + y = - 2$

$- 2 x - 4 y = (- 2) (2)$

$2 x + y = - 2$

$- 2 x - 4 y = (- 2) (2)$

Simplify the right side.

Multiply $- 2$ by $2$ .

$2 x + y = - 2$

$- 2 x - 4 y = - 4$

$2 x + y = - 2$

$- 2 x - 4 y = - 4$

$2 x + y = - 2$

$- 2 x - 4 y = - 4$

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

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

Divide each term in $- 3 y = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 6$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$y = 2$

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 $x$ .

$2 x + 2 = - 2$

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

Subtract $2$ from both sides of the equation.

$2 x = - 2 - 2$

Subtract $2$ from $- 2$ .

$2 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

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

$(- 2, 2)$

Since the system has a point of intersection, the system is independent.

Independent

Determine if Dependent, Independent, or Inconsistent 2x+y=-2 , x+2y=2

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