# Precalculus Examples

,

Step 1

Step 1.1

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

Step 1.2

Simplify.

Step 1.2.1

Simplify the left side.

Step 1.2.1.1

Simplify .

Step 1.2.1.1.1

Apply the distributive property.

Step 1.2.1.1.2

Multiply by .

Step 1.2.2

Simplify the right side.

Step 1.2.2.1

Multiply by .

Step 1.3

Add the two equations together to eliminate from the system.

Step 1.4

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

Infinite number of solutions

Step 1.5

Solve one of the equations for .

Step 1.5.1

Add to both sides of the equation.

Step 1.5.2

Divide each term in by and simplify.

Step 1.5.2.1

Divide each term in by .

Step 1.5.2.2

Simplify the left side.

Step 1.5.2.2.1

Cancel the common factor of .

Step 1.5.2.2.1.1

Cancel the common factor.

Step 1.5.2.2.1.2

Divide by .

Step 1.5.2.3

Simplify the right side.

Step 1.5.2.3.1

Simplify each term.

Step 1.5.2.3.1.1

Divide by .

Step 1.5.2.3.1.2

Cancel the common factor of .

Step 1.5.2.3.1.2.1

Cancel the common factor.

Step 1.5.2.3.1.2.2

Divide by .

Step 1.6

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

Step 2

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

Dependent

Step 3