Where's the other 4 equations?

Algebra Level 5

Let \(a, b, c, x, y, z\) be positive real numbers such that

\[ \begin{align*} abx + bcy + acz &= xyz - 2abc \\ axz + bxy + cyz &= xyz. \\ \end{align*} \]

How many solutions are there to this system?

If there are an infinite number of solutions, input \(-1\) as your answer. If there are no solutions to the system, input \(0\).


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