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First, finding the solution space to some systems is simple. For instance, each equation in the following system
\begin{equation*}
\begin{alignedat}{3}
x \amp \amp \amp {}={} \amp 2 \\
\amp \amp y \amp {}={} \amp -1. \\
\end{alignedat}
\end{equation*}

has only one unknown so we can see that there is exactly one solution, which is \((x,y) = (2,-1)\text{.}\) We call such a system *decoupled*.