Determine if Dependent, Independent, or Inconsistent -x-y=7 , 5x-5y=5

$- x - y = 7$ , $5 x - 5 y = 5$

Step 1

Solve the system of equations.

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

$(5) \cdot (- x - y) = (5) (7)$

$5 x - 5 y = 5$

Simplify.

Simplify the left side.

Simplify $(5) \cdot (- x - y)$ .

Apply the distributive property.

$5 (- x) + 5 (- y) = (5) (7)$

$5 x - 5 y = 5$

Multiply.

Multiply $- 1$ by $5$ .

$- 5 x + 5 (- y) = (5) (7)$

$5 x - 5 y = 5$

Multiply $- 1$ by $5$ .

$- 5 x - 5 y = (5) (7)$

$5 x - 5 y = 5$

$- 5 x - 5 y = (5) (7)$

$5 x - 5 y = 5$

$- 5 x - 5 y = (5) (7)$

$5 x - 5 y = 5$

$- 5 x - 5 y = (5) (7)$

$5 x - 5 y = 5$

Simplify the right side.

Multiply $5$ by $7$ .

$- 5 x - 5 y = 35$

$5 x - 5 y = 5$

$- 5 x - 5 y = 35$

$5 x - 5 y = 5$

$- 5 x - 5 y = 35$

$5 x - 5 y = 5$

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

	$-$	$5$	$x$		$-$	$5$	$y$	$=$	$3$	$5$
$+$		$5$	$x$		$-$	$5$	$y$	$=$		$5$
				$-$	$1$	$0$	$y$	$=$	$4$	$0$

Divide each term in $- 10 y = 40$ by $- 10$ and simplify.

Divide each term in $- 10 y = 40$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{40}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{40}{- 10}$

Divide $y$ by $1$ .

$y = \frac{40}{- 10}$

Simplify the right side.

Divide $40$ by $- 10$ .

$y = - 4$

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 $x$ .

$- 5 x - 5 \cdot - 4 = 35$

Multiply $- 5$ by $- 4$ .

$- 5 x + 20 = 35$

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

Subtract $20$ from both sides of the equation.

$- 5 x = 35 - 20$

Subtract $20$ from $35$ .

$- 5 x = 15$

Divide each term in $- 5 x = 15$ by $- 5$ and simplify.

Divide each term in $- 5 x = 15$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{15}{- 5}$

Divide $x$ by $1$ .

$x = \frac{15}{- 5}$

Simplify the right side.

Divide $15$ by $- 5$ .

$x = - 3$

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

$(- 3, - 4)$

Step 2

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

Independent

Step 3

Determine if Dependent, Independent, or Inconsistent -x-y=7 , 5x-5y=5

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