# Shared Flashcard Set

## Details

Categories of Simultaneous Equations
Identifying solvable sets of equations
4
Mathematics
08/10/2020

Term
 Linear Dependence
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.
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