SOLUTION: Systems of equations can have what 3 types of answers with graphs that look how?

Algebra ->  Systems-of-equations -> SOLUTION: Systems of equations can have what 3 types of answers with graphs that look how?      Log On


   

Question 610320: Systems of equations can have what 3 types of answers with graphs that look how?
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
I can only assume that you are talking about systems of two linear equations. Other types of systems will have a different number of possible solutions.

Case 1: One solution. The graph of this type of system of linear equations will have two lines that intersect at a single point. The coordinates of the single point are the solution.

Case 2: No solutions. The graph of this type of system of linear equations will have two lines that are parallel. They do not intersect.

Case 3: An infinite number of solutions. The graph of this type of system of linear equations will have two lines that lie on top of each other. The coordinates of every point on one line will also be on the "second" line. This means the two equations are, in essence, the same equation.