Ta có :
\(\dfrac{x}{10}=\dfrac{y}{5}\Leftrightarrow\dfrac{x}{20}=\dfrac{y}{10}\)
\(\dfrac{y}{2}=\dfrac{z}{3}\Leftrightarrow\dfrac{y}{10}=\dfrac{z}{15}\)
\(\Leftrightarrow\dfrac{x}{20}=\dfrac{y}{10}=\dfrac{z}{15}\)
\(\Leftrightarrow\dfrac{2x}{40}=\dfrac{3y}{30}=\dfrac{4z}{60}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\dfrac{2x}{40}=\dfrac{3y}{30}=\dfrac{4z}{60}=\dfrac{2x-3y+4z}{40-30+60}=\dfrac{330}{70}=\dfrac{33}{7}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{20}=\dfrac{33}{7}\Leftrightarrow x=\dfrac{660}{7}\\\dfrac{y}{10}=\dfrac{33}{7}\Leftrightarrow y=\dfrac{330}{7}\\\dfrac{z}{15}=\dfrac{33}{7}\Leftrightarrow z=\dfrac{495}{7}\end{matrix}\right.\)
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