Cho (4x-3y)/5=(5y-4z)/3=(3z-5x)/4 và x-y+z=2020. Tìm x, y, z 31/07/2021 Bởi Melody 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: $\begin{array}{l} x – y + z = 2020\\ \Leftrightarrow x – 0 + \frac{{ – 3x}}{5} = 2020\\ \Leftrightarrow \frac{2}{5}x = 2020\\ \Leftrightarrow x = 5050\\ \Rightarrow z = – 2020 \end{array}$ Bình luận
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:
$\begin{array}{l} x – y + z = 2020\\ \Leftrightarrow x – 0 + \frac{{ – 3x}}{5} = 2020\\ \Leftrightarrow \frac{2}{5}x = 2020\\ \Leftrightarrow x = 5050\\ \Rightarrow z = – 2020 \end{array}$