Determine if Dependent, Independent, or Inconsistent y=2x+3 x+y=-3

$y = 2 x + 3$ $x + y = - 3$

Step 1

Solve the system of equations.

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

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

$y - 2 x = 3$

$x + y = - 3$

Reorder $y$ and $- 2 x$ .

$- 2 x + y = 3$

$x + y = - 3$

$- 2 x + y = 3$

$x + y = - 3$

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

$- 2 x + y = 3$

$(- 1) \cdot (x + y) = (- 1) (- 3)$

Simplify.

Simplify the left side.

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

Apply the distributive property.

$- 2 x + y = 3$

$- 1 x - 1 y = (- 1) (- 3)$

Rewrite negatives.

Rewrite $- 1 x$ as $- x$ .

$- 2 x + y = 3$

$- x - 1 y = (- 1) (- 3)$

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

$- 2 x + y = 3$

$- x - y = (- 1) (- 3)$

$- 2 x + y = 3$

$- x - y = (- 1) (- 3)$

$- 2 x + y = 3$

$- x - y = (- 1) (- 3)$

$- 2 x + y = 3$

$- x - y = (- 1) (- 3)$

Simplify the right side.

Multiply $- 1$ by $- 3$ .

$- 2 x + y = 3$

$- x - y = 3$

$- 2 x + y = 3$

$- x - y = 3$

$- 2 x + y = 3$

$- x - y = 3$

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

	$-$	$2$	$x$	$+$	$y$	$=$	$3$
$+$		$-$	$x$	$-$	$y$	$=$	$3$
	$-$	$3$	$x$			$=$	$6$

Divide each term in $- 3 x = 6$ by $- 3$ and simplify.

Divide each term in $- 3 x = 6$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{6}{- 3}$

Divide $x$ by $1$ .

$x = \frac{6}{- 3}$

Simplify the right side.

Divide $6$ by $- 3$ .

$x = - 2$

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 $y$ .

$- 2 \cdot - 2 + y = 3$

Multiply $- 2$ by $- 2$ .

$4 + y = 3$

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

Subtract $4$ from both sides of the equation.

$y = 3 - 4$

Subtract $4$ from $3$ .

$y = - 1$

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

$(- 2, - 1)$

Step 2

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

Independent

Step 3

Determine if Dependent, Independent, or Inconsistent y=2x+3 x+y=-3

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