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MathNet 2019-part-06 — 184 problems (EN–VI) Question 123

Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)

Question 123

Compute the value of the expression $\left(-4 x y z^{-1}\right)^{-2}$ if $x$, $y$ and $z$ are the unknowns in the system
$$
\begin{aligned}
& \frac{2}{x}-\frac{1}{y}+\frac{1}{z}=-3 \\
& \frac{1}{x}-\frac{1}{y}-\frac{1}{z}=3 \\
& \frac{3}{x}+\frac{2}{y}+\frac{2}{z}=4
\end{aligned}
$$