8.2 Matrices and systems of equations

A system of equation with no solution which happens when we solve the system and end up an equation that cannot make any sense mathematically. 
Example 1:

From above, we can notice that it is impossible for 0=4, thus, we can say that the system of equations has NO SOLUTION or inconsistent.

Also, we learned another type of system of equations which is a system with an infinite number of solutions. It always end up with an equation where all the variables are disappeared.

Example 2:

In the last row of matrix, it end up with all zeros on both sides of equation, which means the system of equations have an infinite set of solutions.