Question

\(\dfrac{x}{2}\)=\(\dfrac{y}{3}\); \(\dfrac{y}{5}\)=\(\dfrac{z}{4}\)và 2x + y - 3z = 5

Answer 1

\(\dfrac{x}{2}=\dfrac{y}{3}\Leftrightarrow\dfrac{x}{10}=\dfrac{y}{15}\left(1\right)\)

\(\dfrac{y}{5}=\dfrac{z}{4}\Leftrightarrow\dfrac{y}{15}=\dfrac{z}{12}\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{12}\)

\(\Leftrightarrow\dfrac{2x}{20}=\dfrac{y}{15}=\dfrac{3z}{36}\)

Theo t,c dãy tỉ số bằng nhau ta có :

\(\dfrac{2x}{20}=\dfrac{y}{15}=\dfrac{3z}{36}=\dfrac{2x+y-3z}{20+15-36}=\dfrac{5}{-1}=-5\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x}{20}=-5\\\dfrac{y}{15}=-5\\\dfrac{3z}{36}=-5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-50\\y=-75\\z=-60\end{matrix}\right.\)

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