Question

Tìm x, y, z biết rằng:

\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\) và \(5z-3x-4y=50\)

Answer 1

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

\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\)

\(\Rightarrow\dfrac{5z-25}{30}=\dfrac{3x-3}{6}=\dfrac{4y+12}{16}\\ =\dfrac{\left(5z-25\right)-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}\\ =\dfrac{5z-25-3x+3-4y-12}{8}\\ =\dfrac{5z-3x-4y-34}{8}\\ \dfrac{50-34}{8}=2\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{5z-25}{30}=2\\\dfrac{3x-3}{6}=2\\\dfrac{4y+12}{16}=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}5z=85\\3x=15\\4y=20\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}z=17\\x=5\\y=5\end{matrix}\right.\)