Giải thích các bước giải:

$\begin{array}{l} \frac{{2z - 4y}}{5} = \frac{{5y - 3x}}{4} = \frac{{4x - 5z}}{3}\\  \Rightarrow \left\{ \begin{array}{l} \frac{{2z - 4y}}{5} = \frac{{5y - 3x}}{4}\\ \frac{{5y - 3x}}{4} = \frac{{4x - 5z}}{3} \end{array} \right.\\  \Rightarrow \left\{ \begin{array}{l} \frac{{2z}}{5} + \frac{{3x}}{4} = \frac{{41y}}{{20}}\\ \frac{{5y}}{4} + \frac{{5z}}{3} = \frac{{25x}}{{12}} \end{array} \right.\\  \Rightarrow \left\{ \begin{array}{l} \frac{{8z}}{{41}} + \frac{{15x}}{{41}} = y\\ \frac{5}{4}(\frac{{8z}}{{41}} + \frac{{15x}}{{41}}) + \frac{{5z}}{3} = \frac{{25x}}{{12}} \end{array} \right.\\  \Rightarrow \left\{ \begin{array}{l} \frac{{8z}}{{41}} + \frac{{15x}}{{41}} = y\\ \frac{{235z}}{{123}} = \frac{{200x}}{{123}} \end{array} \right.\\  \Rightarrow \left\{ \begin{array}{l} \frac{{5z}}{8} = y\\ \frac{{47z}}{{40}} = x \end{array} \right. \end{array}$

$\begin{array}{l} {x^2} - {z^2} = 36\\  \Leftrightarrow {(\frac{{47}}{{40}}z)^2} - {z^2} = 36\\  \Leftrightarrow \frac{{609}}{{1600}}{z^2} = 36\\  \Leftrightarrow z = \frac{{80\sqrt 3 }}{{\sqrt {203} }}\\  \Rightarrow \left\{ \begin{array}{l} y = \frac{{50\sqrt 3 }}{{\sqrt {203} }}\\ x = \frac{{94\sqrt 3 }}{{\sqrt {203} }} \end{array} \right. \end{array}$