Determine if Dependent, Independent, or Inconsistent 2x=y+3 y=-2x+1

$2 x = y + 3$ $y = - 2 x + 1$

Step 1

Solve the system of equations.

Subtract $y$ from both sides of the equation.

$2 x - y = 3$

$y = - 2 x + 1$

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

Add $2 x$ to both sides of the equation.

$y + 2 x = 1$

$2 x - y = 3$

Reorder $y$ and $2 x$ .

$2 x + y = 1$

$2 x - y = 3$

$2 x + y = 1$

$2 x - y = 3$

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

	$2$	$x$	$-$	$y$	$=$	$3$
$+$	$2$	$x$	$+$	$y$	$=$	$1$
	$4$	$x$			$=$	$4$

Divide each term in $4 x = 4$ by $4$ and simplify.

Divide each term in $4 x = 4$ by $4$ .

$\frac{4 x}{4} = \frac{4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{4}{4}$

Divide $x$ by $1$ .

$x = \frac{4}{4}$

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$

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 $y$ .

$2 (1) - y = 3$

Multiply $2$ by $1$ .

$2 - y = 3$

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

Subtract $2$ from both sides of the equation.

$- y = 3 - 2$

Subtract $2$ from $3$ .

$- y = 1$

Divide each term in $- y = 1$ by $- 1$ and simplify.

Divide each term in $- y = 1$ by $- 1$ .

$\frac{- y}{- 1} = \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{1}{- 1}$

Divide $y$ by $1$ .

$y = \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$y = - 1$

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

$(1, - 1)$

Step 2

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

Independent

Step 3

Determine if Dependent, Independent, or Inconsistent 2x=y+3 y=-2x+1

Related Questions

Support LCMGCF.com by disabling your adblocker.