Question

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Answer 1

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 \(2x+y=7\).

Answer 2

I would start by making \(y\) a function of \(x\). So we have \(y(x) = -2x+7\). I would then plug in each possible \(x\).

Answer 3

\[
x=1 \implies y = 5 \\
x=2 \implies y = 3 \\
x=3 \implies y = 1
\]So the answers we get is: \[F = \{(1, 5), (2,3), (3,1)\}\]

Answer 4

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.

Answer 5

Okay thanks my internet connection sucks so it took me long to see this and respond to you... :)