Trang chủ » Hỏi đáp » Môn Toán `2x = 3y = 4z và 5x – 5x = -6` 30/03/2024 `2x = 3y = 4z và 5x – 5x = -6`
Giải đáp: $x = – \dfrac{{18}}{5};y = – \dfrac{{12}}{5};z = – \dfrac{9}{5}$ Lời giải và giải thích chi tiết: $\begin{array}{l}2x = 3y = 4z;5x – 5y = – 6\\ \Leftrightarrow x – y = – \dfrac{6}{5}\\ \Leftrightarrow \dfrac{{2x}}{{12}} = \dfrac{{3y}}{{12}} = \dfrac{{4z}}{{12}}\\ \Leftrightarrow \dfrac{x}{6} = \dfrac{y}{4} = \dfrac{z}{3} = \dfrac{{x – y}}{{6 – 4}} = \dfrac{{ – \dfrac{6}{5}}}{2} = – \dfrac{3}{5}\\ \Leftrightarrow \left\{ \begin{array}{l}x = – \dfrac{3}{5}.6 = – \dfrac{{18}}{5}\\y = – \dfrac{3}{5}.4 = – \dfrac{{12}}{5}\\z = – \dfrac{3}{5}.3 = – \dfrac{9}{5}\end{array} \right.\\Vậy\,x = – \dfrac{{18}}{5};y = – \dfrac{{12}}{5};z = – \dfrac{9}{5}\end{array}$ Trả lời
2x = 3y = 4z;5x – 5y = – 6\\
\Leftrightarrow x – y = – \dfrac{6}{5}\\
\Leftrightarrow \dfrac{{2x}}{{12}} = \dfrac{{3y}}{{12}} = \dfrac{{4z}}{{12}}\\
\Leftrightarrow \dfrac{x}{6} = \dfrac{y}{4} = \dfrac{z}{3} = \dfrac{{x – y}}{{6 – 4}} = \dfrac{{ – \dfrac{6}{5}}}{2} = – \dfrac{3}{5}\\
\Leftrightarrow \left\{ \begin{array}{l}
x = – \dfrac{3}{5}.6 = – \dfrac{{18}}{5}\\
y = – \dfrac{3}{5}.4 = – \dfrac{{12}}{5}\\
z = – \dfrac{3}{5}.3 = – \dfrac{9}{5}
\end{array} \right.\\
Vậy\,x = – \dfrac{{18}}{5};y = – \dfrac{{12}}{5};z = – \dfrac{9}{5}
\end{array}$