Determine if Dependent, Independent, or Inconsistent y=x-5 -2x+2y=-10

$y = x - 5$ $- 2 x + 2 y = - 10$

Step 1

Solve the system of equations.

Move all terms containing variables to the left side of the equation.

Subtract $x$ from both sides of the equation.

$y - x = - 5$

$- 2 x + 2 y = - 10$

Reorder $y$ and $- x$ .

$- x + y = - 5$

$- 2 x + 2 y = - 10$

$- x + y = - 5$

$- 2 x + 2 y = - 10$

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

$(- 2) \cdot (- x + y) = (- 2) (- 5)$

$- 2 x + 2 y = - 10$

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 (- x) - 2 y = (- 2) (- 5)$

$- 2 x + 2 y = - 10$

Multiply $- 1$ by $- 2$ .

$2 x - 2 y = (- 2) (- 5)$

$- 2 x + 2 y = - 10$

$2 x - 2 y = (- 2) (- 5)$

$- 2 x + 2 y = - 10$

$2 x - 2 y = (- 2) (- 5)$

$- 2 x + 2 y = - 10$

Simplify the right side.

Multiply $- 2$ by $- 5$ .

$2 x - 2 y = 10$

$- 2 x + 2 y = - 10$

$2 x - 2 y = 10$

$- 2 x + 2 y = - 10$

$2 x - 2 y = 10$

$- 2 x + 2 y = - 10$

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

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

Since $0 = 0$ , the equations intersect at an infinite number of points.

Infinite number of solutions

Solve one of the equations for $y$ .

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

$- 2 y = 10 - 2 x$

Divide each term in $- 2 y = 10 - 2 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 10 - 2 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- 2 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- 2 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{10}{- 2} + \frac{- 2 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 2$ .

$y = - 5 + \frac{- 2 x}{- 2}$

Cancel the common factor of $- 2$ .

Cancel the common factor.

$y = - 5 + \frac{- 2 x}{- 2}$

Divide $x$ by $1$ .

$y = - 5 + x$

The solution is the set of ordered pairs that make $y = - 5 + x$ true.

$(x, - 5 + x)$

Step 2

Since the system is always true, the equations are equal and the graphs are the same line. Thus, the system is dependent.

Dependent

Step 3

Determine if Dependent, Independent, or Inconsistent y=x-5 -2x+2y=-10

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