# Precalculus Examples

,

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

Simplify.

Simplify the left side.

Simplify .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Simplify the right side.

Multiply by .

Add the two equations together to eliminate from the system.

Since , the equations intersect at an infinite number of points.

Infinite number of solutions

Solve one of the equations for .

Add to both sides of the equation.

Divide each term in by and simplify.

Divide each term in by .

Simplify the left side.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify the right side.

Simplify each term.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

The solution is the set of ordered pairs that make true.

Since the system is always true, the equations are equal and the graphs are the same line. Thus, the system is dependent.

Dependent