Determine if Dependent, Independent, or Inconsistent y=x+4 y=2x+4

$y = x + 4$ $y = 2 x + 4$

Step 1

Solve the system of equations.

Move all terms containing variables to the left.

Subtract $x$ from both sides of the equation.

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

Subtract $2 x$ from both sides of the equation.

$y - x = 4, y - 2 x = 4$

Reorder the polynomial.

$- x + y = 4$

$y - 2 x = 4$

Reorder the polynomial.

$- 2 x + y = 4$

$- x + y = 4$

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

$- x + y = 4$

$(- 1) \cdot (- 2 x + y) = (- 1) (4)$

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- x + y = 4$

$- 1 (- 2 x) - 1 y = (- 1) (4)$

Simplify the expression.

Multiply $- 2$ by $- 1$ .

$- x + y = 4$

$2 x - 1 y = (- 1) (4)$

Rewrite $- 1 y$ as $- y$ .

$- x + y = 4$

$2 x - y = (- 1) (4)$

$- x + y = 4$

$2 x - y = (- 1) (4)$

$- x + y = 4$

$2 x - y = (- 1) (4)$

$- x + y = 4$

$2 x - y = (- 1) (4)$

Simplify the right side.

Multiply $- 1$ by $4$ .

$- x + y = 4$

$2 x - y = - 4$

$- x + y = 4$

$2 x - y = - 4$

$- x + y = 4$

$2 x - y = - 4$

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

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

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 $y$ .

$- (0) + y = 4$

Simplify $- (0) + y$ .

Multiply $- 1$ by $0$ .

$0 + y = 4$

Add $0$ and $y$ .

$y = 4$

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

$(0, 4)$

Step 2

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

Independent

Step 3

Determine if Dependent, Independent, or Inconsistent y=x+4 y=2x+4

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