Cho (4x-3y)/5=(5y-4z)/3=(3z-5x)/4 và x-y+z=2020. Tìm x, y, z

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:

$\begin{array}{l} x – y + z = 2020\\  \Leftrightarrow x – 0 + \frac{{ – 3x}}{5} = 2020\\  \Leftrightarrow \frac{2}{5}x = 2020\\  \Leftrightarrow x = 5050\\  \Rightarrow z =  – 2020 \end{array}$