What happens in a system of equations when the number of equations != number of unknowns?

ossidianaZ

ossidianaZ

Answered question

2021-02-25

What happens in a system of equations when the number of equations number of unknowns?

Answer & Explanation

Latisha Oneil

Latisha Oneil

Skilled2021-02-26Added 100 answers

Step 1
A system of equations is a set or collection of equations that you deal with all together at once. A solution of a linear system is of values to the variables x1x2,x3,,xn such that each of the equations is satisfied. The set of all possible solutions is called the solution set.
A linear system may have in any one of three possible solution-
1.The system has infinitely many solutions.
2.The system has a single unique solution.
3.The system has no solution.
Step 2
The behavior of a linear system is determined by the relationship between the number of equations and the number of unknowns.
-In general, a system with fewer equations than unknowns has infinitely many solutions. Such a system is known as an under determined system.
-In general, a system with the same number of equations and unknowns has a single unique solution.
-In general, a system with more equations than unknowns has no solution. Such a system is also known as an over determined system.
Hence, "a system of equations when the number of equations number of unknowns", then either no solution or infinitely many solution.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?