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# Consider this system of simultaneous equations

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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, c = -6z

Given that (x, y, z) is a solution to the original system of equations, determine all distinct possible values of x+y.

(Please list all the possible values)

May 28, 2022