Giải thích các bước giải:
$\begin{array}{l} \frac{{4x - 3y}}{5} = \frac{{5y - 4z}}{3} = \frac{{3x - 5z}}{4}\\ \Rightarrow \left\{ \begin{array}{l} \frac{{4x}}{5} + \frac{{4z}}{3} = \frac{{34y}}{{15}}\\ \frac{{5y}}{3} - \frac{{3x}}{4} = \frac{z}{{12}} \end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l} \frac{{4x}}{5} + \frac{4}{3}(20y - 9x) = \frac{{34y}}{{15}}\\ 20y - 9x = z \end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l} \frac{{ - 56x}}{5} = \frac{{ - 122y}}{{15}}\\ 20y - 9x = z \end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l} x = \frac{{61y}}{{84}}\\ 20y - 9x = z \end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l} x = \frac{{61y}}{{84}}\\ 20y - 9.\frac{{61y}}{{84}} = z \end{array} \right.\\ \Rightarrow \left\{ \begin{array}{l} x = \frac{{61y}}{{84}}\\ \frac{{377}}{{28}}y = z \end{array} \right. \end{array}$
Khi đó:
$\begin{array}{l} x - y + z = 2020\\ \Leftrightarrow x - 0 + \frac{{ - 3x}}{5} = 2020\\ \Leftrightarrow \frac{2}{5}x = 2020\\ \Leftrightarrow x = 5050\\ \Rightarrow z = - 2020 \end{array}$
