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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.
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