Question 743668: If a system of linear equations intersects at every point what does that mean?
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
If these two or more linear equations  , that point of intersection is called the  to the system of linear equations.
How many solutions can systems of linear equations have?
Case I:  solution
This is the most common situation and it involves lines that intersect  time.
Case 2:  
This only happens when the lines are  . As you can see, parallel lines are  going to   .
Case 3: 
This is the  case and only occurs when you have the   .
Consider, for instance, the two lines below
 and
These two equations are really the line.
Example of a system that has infinite solutions:
Line 1: 
find  and 
set  and find
 =>  ; so, is at ( ,)
set  and find 
 =>  =>  ; so, is at ( ,)
Line 2: 
set and find
 =>  =>  ; so, is at (,)
set and find
 =>  =>  => ; so, is at (,)
on a graph you will see only one line:
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