# How does a system of linear equations have no solution?

##### 1 Answer

I tried this:

#### Explanation:

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!

Example:

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!