Suppose that $x, y, z$ are non-zero real numbers such that $$\begin{cases}x = 2 - \dfrac{y}{z} \\ \\ y = 2 -\dfrac{z}{x} \\ \\ z = 2 -\dfrac{x}{y}.\end{cases}$$Find all possible values of $T = x + y + z$
Source: 2019 Saudi Arabia January Camp Test 1.1
Tags: algebra, system of equations
Suppose that $x, y, z$ are non-zero real numbers such that $$\begin{cases}x = 2 - \dfrac{y}{z} \\ \\ y = 2 -\dfrac{z}{x} \\ \\ z = 2 -\dfrac{x}{y}.\end{cases}$$Find all possible values of $T = x + y + z$