7)
\(\dfrac{x}{4}=\dfrac{y}{-3}=\dfrac{z}{5}\)
=>\(\dfrac{x}{4}=\dfrac{-6y}{18}=\dfrac{7z}{35}=\dfrac{x-6y-7z}{4+18-35}=\dfrac{39}{-13}=-3\)
x=-12
y=9
z=-15
8)
\(\dfrac{x}{3}=\dfrac{y}{7}=\dfrac{z}{-9}\)
=>\(\dfrac{2x}{6}=\dfrac{4y}{28}=\dfrac{-7z}{63}=\dfrac{2x+4y-7z}{6+28+63}=\dfrac{97}{97}=1\)
x=3
y=7
z=-9
15: Đặt \(\dfrac{x}{5}=\dfrac{y}{2}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=5k\\y=2k\end{matrix}\right.\)
Ta có: \(x^2\cdot y^2=100\)
\(\Leftrightarrow100k^2=100\)
\(\Leftrightarrow k^2=1\)
Trường hợp 1: k=1
\(\Leftrightarrow\left\{{}\begin{matrix}x=5k=5\\y=2k=2\end{matrix}\right.\)
Trường hợp 2: k=-1
\(\Leftrightarrow\left\{{}\begin{matrix}x=5k=-5\\y=2k=-2\end{matrix}\right.\)
