Term

Definition
Definition: when one equation in a system can be expressed as a combination of the other equations.
Example: in the system of equations shown below, eq. (3) is not independent, since (3) = 2 × (2) + (1).
(1) x + y + z = 10
(2) x + 2y + z = 12
(3) 3x + 5y + 3z = 34 


Term
Overdetermined System of Equations 

Definition
Definition: system with m equations and n unknowns where m > n.
In general there will be no consistent solution for all m equations, though some systems like this may have a solution. 


Term
Underdetermined System of Equations 

Definition
Definition: system with m equations and n unknowns where m < n.
There are not enough constraints for the n unknowns, so there are infinitely many possible solutions. 


Term
Exactly Determined System of Equations 

Definition
Definition: system with m equations and n unknowns where m = n and the equations are linearly independent. 

