How does a system of linear equations have no solution?
I tried this:
To visualize this situation we can use a simple example:
Consider two linear equations in
Solving a system involving these two equations can lead us to find, for example, one solution...but what does this means?
We find a set of coordinates
It can happen that the two lines do not cross....the lines are parallel. In this case we cannot find a point in common between the two and consequently the system of the two equations representing the two lines will not give us a solution!
consider the two equations:
if you try to solve the system of these two equations (by substitution, for example) you'll get a strange situation....no solutions!
If you plot the two lines corresponding to the two equations you will see that they are parallel!