# Algebra Examples

,

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

Simplify.

Simplify .

Apply the distributive property.

Multiply by .

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 by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Divide by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

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