# Precalculus Examples

Determine if Dependent, Independent, or Inconsistent
,
Solve the system of equations.
Move all terms containing variables to the left side of the equation.
Move to the left side of the equation because it contains a variable.
Move .
Move all terms containing variables to the left side of the equation.
Move to the left side of the equation because it contains a variable.
Reorder and .
Move to the right side of the equation because it does not contain a variable.
Add the two equations together to eliminate from the system.
Divide each term by and simplify.
Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Simplify the expression.
Multiply by to get .
Rewrite as .
Divide by to get .
Substitute the value found for into one of the original equations, then solve for .
Substitute the value found for into one of the original equations to solve for .
Multiply by to get .
Move all terms not containing to the right side of the equation.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Subtract from to get .
Multiply each term in by
Multiply each term in by .
Simplify .
Multiply by to get .
Multiply by to get .
Multiply by to get .
The solution to the independent system of equations can be represented as a point.
Since the system has a point of intersection, the system is independent.
Independent

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