\begin{definition}[Definition:Simultaneous Equations/Consistency]
A system of simultaneous equations:
:$\forall i \in \set {1, 2, \ldots m} : \map {f_i} {x_1, x_2, \ldots x_n} = \beta_i$
that has at least one solution is '''consistent'''.
If a system has no solutions, it is '''inconsistent'''.
Category:Definitions/Simultaneous Equations
\end{definition}