In this problem, we will consider this system of simultaneous equations:
\($$\begin{array}{r@{~}c@{~}l l} 3x+5y-6z &=&2, & \textrm{(i)} \\ 5xy-10yz-6xz &=& -41, & \textrm{(ii)} \\ xyz&=&6. & \textrm{(iii)} \end{array}\)
Let a=3x, b=5y, and c=-6z.
Given that (x,y,z) is a solution to the original system of equations, determine all distinct possible values of x+y.
