Determine if Dependent, Independent, or Inconsistent y=x+4 , y=-x-4

$y = x + 4$ , $y = - x - 4$

Solve the system of equations.

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Subtract $x$ from both sides of the equation.

$y - x = 4$

$y = - x - 4$

Add $x$ to both sides of the equation.

$y - x = 4$

$y + x = - 4$

Reorder the polynomial.

$- x + y = 4$

$y + x = - 4$

Reorder the polynomial.

$- x + y = 4$

$x + y = - 4$

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

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

Divide each term by $2$ and simplify.

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Divide each term in $2 y = 0$ by $2$ .

$\frac{2 y}{2} = \frac{0}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 y}{2} = \frac{0}{2}$

Divide $y$ by $1$ .

$y = \frac{0}{2}$

Divide $0$ by $2$ .

$y = 0$

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

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Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$- x + 0 = 4$

Add $- x$ and $0$ .

$- x = 4$

Multiply each term in $- x = 4$ by $- 1$

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Multiply each term in $- x = 4$ by $- 1$ .

$(- x) \cdot - 1 = 4 \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x = 4 \cdot - 1$

Multiply $x$ by $1$ .

$x = 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$x = - 4$

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

$(- 4, 0)$

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

Independent

Determine if Dependent, Independent, or Inconsistent y=x+4 , y=-x-4