1. The problem statement, all variables and given/known data (1/7)x + (1/11)y = 1 and (6/7)x =(10/11)y 3. The attempt at a solution I'm doing this problem and we have to do it based on speculated babylonian approach which involves setting x and y equal half the semiperimeter and plus or minus a change in the side of lengths, i/e x = a/2 + z y = a/2 - z I'm also trying to really understand this problem area wise, like how it could've been solved involving quadratics. when I insert the respective formulas (1/7)(1/2 + z) + 1/11(1/2 - z) = 1 i get x = 35/2 and y = -33/2 this isnt the answer in the book, which is x = 35/4 and y = 33/4 how can I use the relation of (x - y)^2 = (x +y)^2 - 4xy does it allow to write (6/7x - 10/11y)^2 = (1/7x + 1/11y)^2 - 4xy? i know how to find the answer through substitutions but babylonians used the above identy in early multiplication also, is it possible to construct a "completing the square" diagram in this problem? thanks!