Explain what is meant by the terms Consistent Dependent Cons

Explain what is meant by the terms Consistent Dependent, Consistent Independent, and Inconsistent as applied to systems of linear equations. Give an example of a system of one of these types and explain why it is of that type

Solution

Systems of linear equations is a collection of two or more linear equations.

Now the solution of this system can be of three type:

1. exact one solution

2. more than one solution.

3. No solution.

Now if a system has exactly one solution, than the system is said to be Consistent Independent.

Now if a system has more than one solution, than the system is said to be Consistent Dependent.

Now if a system has no solutions, than the system is said to be Inconsistent.

Eg.

x + y = 2

x - y = 2

Systems solution is (x, y) = (2, 0)

Since system has exatly one solution, So it will be Consistent Independent.