Video: Figuring the Sum of Elements of a Set given Its Cartesian Product with a given Set

If {31} Γ— {π‘₯, 𝑦} = {(31, 25) (31, 46)}, find all the possible values of π‘₯ + 𝑦.

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Video Transcript

If the set 31 times the set π‘₯ 𝑦 is equal to the set 31 25, 31 46, find all possible values of π‘₯ plus 𝑦.

Our first set is 31, and our second that is π‘₯ plus 𝑦. We’re also given the ordered pair set of their product. If we’re multiplying 31 by the set π‘₯ 𝑦 and it produces 31 25, 31 46, we know that π‘₯ is equal to 25 and 𝑦 equals 46.

π‘₯ plus 𝑦 is then equal to 25 plus 46, which equals 71. It’s also possible that we could switch the π‘₯ and 𝑦 values, in which case π‘₯ plus 𝑦 would be equal to 46 plus 25 and the solution would still be equal to 71. The only possible outcome of π‘₯ plus 𝑦 here is 71.

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