 # What happens in a system of equations when the number of equations != number of unknowns? ossidianaZ 2021-02-25 Answered
What happens in a system of equations when the number of equations $\ne$ number of unknowns?
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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 ${x}_{1}{x}_{2},{x}_{3},\dots ,{x}_{n}$ 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 $\ne$ number of unknowns", then either no solution or infinitely many solution.