Solutions of a system

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

Examples:

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

Examples:

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

A degenerate equation has the form:

0x₁ + 0x₂ + ….. + 0x_n = b

Then:

–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