Solutions of a system

A solution of the system is a solution of all the equations.


To solve a system is to find all of its solutions.
Depending on the number of solutions, we can classify the systems:
–Consistent systems: if there is at least one solution. They can be:
          · Independent systems: there is one solution
          · Dependent systems: there are infinite solutions
–Inconsistent systems: if there is no solution

NOTE#1: A homogeneous system has always a solution.

A degenerate equation has the form:

          0x1 + 0x2 + ….. + 0xn = b


–If b = 0, it is called trivial equation

–If b ≠ 0, it is called absurd equation


NOTE#2: if there is an absurd equation in a system then it is an inconsistent system


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