Question

Tìm x,y,z biết: \(\dfrac{x}{10}=\dfrac{y}{15},x=\dfrac{z}{2},x+2y-3z=-24\)

Answer 1

\(\dfrac{x}{10}=\dfrac{y}{15}\) (1)

\(x=\dfrac{z}{2}\Rightarrow\dfrac{x}{1}=\dfrac{z}{2}\Rightarrow\dfrac{x}{10}=\dfrac{z}{20}\) (2)

Từ (1) và (2) \(\Rightarrow\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{20}\)

Áp dụng tính chất dãy tỉ số bằng nhau, ta có:

\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{20}=\dfrac{x+2y-3z}{10+30-60}=\dfrac{-24}{-20}=\dfrac{6}{5}\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{10}=\dfrac{6}{5}\Rightarrow x=\dfrac{6}{5}\cdot10=12\\\dfrac{y}{15}=\dfrac{6}{5}\Rightarrow y=\dfrac{6}{5}\cdot15=18\\\dfrac{z}{20}=\dfrac{6}{5}\Rightarrow y=\dfrac{6}{5}\cdot20=24\end{matrix}\right.\)

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