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So \(x \in \{1, 2, 3\}\) and \(y\in \{1, 2, 3, 4, 5, 6, 7\}\). You want to find every pair that fits the equality \(2x+y=7\).
I would start by making \(y\) a function of \(x\). So we have \(y(x) = -2x+7\). I would then plug in each possible \(x\).

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\[ x=1 \implies y = 5 \\ x=2 \implies y = 3 \\ x=3 \implies y = 1 \]So the answers we get is: \[F = \{(1, 5), (2,3), (3,1)\}\]
A general heuristic I can see being useful is to make the larger set be a function of the smaller set, because you have to do less plugging stuff in.
Okay thanks my internet connection sucks so it took me long to see this and respond to you... :)

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