\begin{definition}[Definition:Simultaneous Equations]
A '''system of simultaneous equations''' is a set of equations:
:$\forall i \in \set {1, 2, \ldots, m} : \map {f_i} {x_1, x_2, \ldots x_n} = \beta_i$
That is:
{{begin-eqn}}
{{eqn | l = \beta_1
      | r = \map {f_1} {x_1, x_2, \ldots x_n}
}}
{{eqn | l = \beta_2
      | r = \map {f_2} {x_1, x_2, \ldots x_n}
}}
{{eqn | o = \cdots}}
{{eqn | l = \beta_m
      | r = \map {f_m} {x_1, x_2, \ldots x_n}
}}
{{end-eqn}}
\end{definition}