Question Video: Figuring the Sum of Elements of a Set given Its Cartesian Product with a given Set Mathematics • Third Year of Preparatory School

Video Transcript

If the set 31 times the set 𝑥 𝑦 is equal to the set 31 25, 31 46, find all possible values of 𝑥 plus 𝑦.

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

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