# 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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