Determine if Dependent, Independent, or Inconsistent 2x+2y=6 2x-2y=6

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

Step 1

Solve the system of equations.

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

$(- 1) \cdot (2 x + 2 y) = (- 1) (6)$

$2 x - 2 y = 6$

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (2 x + 2 y)$ .

Apply the distributive property.

$- 1 (2 x) - 1 (2 y) = (- 1) (6)$

$2 x - 2 y = 6$

Multiply.

Multiply $2$ by $- 1$ .

$- 2 x - 1 (2 y) = (- 1) (6)$

$2 x - 2 y = 6$

Multiply $2$ by $- 1$ .

$- 2 x - 2 y = (- 1) (6)$

$2 x - 2 y = 6$

$- 2 x - 2 y = (- 1) (6)$

$2 x - 2 y = 6$

$- 2 x - 2 y = (- 1) (6)$

$2 x - 2 y = 6$

$- 2 x - 2 y = (- 1) (6)$

$2 x - 2 y = 6$

Simplify the right side.

Multiply $- 1$ by $6$ .

$- 2 x - 2 y = - 6$

$2 x - 2 y = 6$

$- 2 x - 2 y = - 6$

$2 x - 2 y = 6$

$- 2 x - 2 y = - 6$

$2 x - 2 y = 6$

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

	$-$	$2$	$x$	$-$	$2$	$y$	$=$	$-$	$6$
$+$		$2$	$x$	$-$	$2$	$y$	$=$		$6$
				$-$	$4$	$y$	$=$		$0$

Divide each term in $- 4 y = 0$ by $- 4$ and simplify.

Divide each term in $- 4 y = 0$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{0}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{0}{- 4}$

Divide $y$ by $1$ .

$y = \frac{0}{- 4}$

Simplify the right side.

Divide $0$ by $- 4$ .

$y = 0$

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 $x$ .

$- 2 x - 2 \cdot 0 = - 6$

Simplify $- 2 x - 2 \cdot 0$ .

Multiply $- 2$ by $0$ .

$- 2 x + 0 = - 6$

Add $- 2 x$ and $0$ .

$- 2 x = - 6$

Divide each term in $- 2 x = - 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 6}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 2}$

Simplify the right side.

Divide $- 6$ by $- 2$ .

$x = 3$

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

$(3, 0)$

Step 2

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

Independent

Step 3

Determine if Dependent, Independent, or Inconsistent 2x+2y=6 2x-2y=6

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