Determine if Dependent, Independent, or Inconsistent -x-2y=-7 , 5x-y=2

$- x - 2 y = - 7$ , $5 x - y = 2$

Step 1

Solve the system of equations.

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

$- x - 2 y = - 7$

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

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (5 x - y)$ .

Apply the distributive property.

$- x - 2 y = - 7$

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

Multiply.

Multiply $5$ by $- 2$ .

$- x - 2 y = - 7$

$- 10 x - 2 (- y) = (- 2) (2)$

Multiply $- 1$ by $- 2$ .

$- x - 2 y = - 7$

$- 10 x + 2 y = (- 2) (2)$

$- x - 2 y = - 7$

$- 10 x + 2 y = (- 2) (2)$

$- x - 2 y = - 7$

$- 10 x + 2 y = (- 2) (2)$

$- x - 2 y = - 7$

$- 10 x + 2 y = (- 2) (2)$

Simplify the right side.

Multiply $- 2$ by $2$ .

$- x - 2 y = - 7$

$- 10 x + 2 y = - 4$

$- x - 2 y = - 7$

$- 10 x + 2 y = - 4$

$- x - 2 y = - 7$

$- 10 x + 2 y = - 4$

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

			$-$	$x$	$-$	$2$	$y$	$=$	$-$	$7$
$+$	$-$	$1$	$0$	$x$	$+$	$2$	$y$	$=$	$-$	$4$
	$-$	$1$	$1$	$x$				$=$	$-$	$1$	$1$

Divide each term in $- 11 x = - 11$ by $- 11$ and simplify.

Divide each term in $- 11 x = - 11$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{- 11}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{- 11}{- 11}$

Divide $x$ by $1$ .

$x = \frac{- 11}{- 11}$

Simplify the right side.

Divide $- 11$ by $- 11$ .

$x = 1$

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 $y$ .

$- (1) - 2 y = - 7$

Multiply $- 1$ by $1$ .

$- 1 - 2 y = - 7$

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

Add $1$ to both sides of the equation.

$- 2 y = - 7 + 1$

Add $- 7$ and $1$ .

$- 2 y = - 6$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $- 2$ .

$y = 3$

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

$(1, 3)$

Step 2

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

Independent

Step 3

Determine if Dependent, Independent, or Inconsistent -x-2y=-7 , 5x-y=2

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