Types of Solutions

1.) Consistent
                 - If one variable can be eliminated
                   ex. 
                         x + y = 5 ,  x + y = 7
the graph would look like this :

2.) Consistent with infinite solution
                 - is the same but have multiples of  "n" same slope , x & y intercepts
              ex.
                   2x +  2y = 2                                  4x + 4y = 4

 

their graphs would look like this we cant see the red one because most infinite solutions are the same





3.) Inconsistent 
                 - Cannot find the value of x+y
                  - no variable is left

 4.) Parameter 
                 - to limit the infinite solutions

What is a parameter?

• A rule or a limit that controls what something is or how should be done
• an arbitrary constant who's value characterizes a member of a system ( as a family of curves ) also; a quantity  ( as a mean or variance ) that describes a statistical population 
• An independent variable used to express the coordinates of a variable and functions of them