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[Music] here were going to look at a nice non-linear system of equations we want to solve it over the real numbers so the first equation is x minus 1 times y minus 1 times z minus 1 equals x y z minus one and then the second one is x minus two times y minus two times z minus two equals x y z minus two there are a couple of hints built into the wording of this problem first we want to notice there are three variables but only two equations and that means there must be some sort of trick in order for there to be only one solution here but i want to be very careful to say that a priori we dont know there is only one solution there could be zero solutions or infinitely many solutions it just turns out that the fact is that usually with problems like this there is only one solution so that means we should keep our eye out for a trick that somehow reduces this system so that theres only one obvious solution okay so lets maybe jump into this starting with this red dot equation so im goi