# Have You Tried Swapping The Positions?

Algebra Level 3

$\large{ \begin{cases} ax+a^2y + z = 0 \\ bx+b^2y + z = 0 \\ cx + c^2 y + z = 0 \end{cases}}$

If the system of equations above has exactly one trivial solution, $$(0,0,0)$$, and that the constant non-zero coefficients $$a,b,c$$ follows a geometric progression then the common ratio cannot be $$\text{______}$$.

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