Is rst = 1?

Cydney Seigerman, Magoosh Tutor

Subtracting one equation from the other is actually OK to do. And you're correct that after subtracting, we can factor out an s, leaving us with the following expression.

s(r-t) = 0

While this algebra gives us two possible answers (s=0 or r-t =0), before concluding that these are two valid solutions, it's necessary to check these responses against the initial conditions of the question. Since we have combined the statements, we must consider both:

1. rs = 1
2. st = 1

In both cases, s?0. If s=0, then the product of s with any number would also have to equal 0. However, statements 1 and 2 indicate that the product of s and another number is not 0. Based on this analysis, we can determine that the possible solution s=0 is not a valid solution for the problem. We are therefore left with the other solution, r-t = 0, from which we can conclude that r=t. Since r and t can equal any number, as long as they equal the same number, we cannot say for sure if rst=1.

I hope this helps :)

Jan 4, 2016 • Reply