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Physics

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    $\begingroup$ "But if that's the case you'll find there is only one solution for $I$ and $V$" Technically for given values of $P$ and $R$, you will get a system of two equations in two variables. This system of equations might have a single solution. $\endgroup$ Commented Dec 3, 2016 at 1:33
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    $\begingroup$ Specifically, there is a solution for the system of equations if $PR \ge 0$. That is, both $P$ and $R$ have the same sign. In most physical situations, they are both positive, so this requirement will be met. $\endgroup$ Commented Dec 3, 2016 at 1:37