Ta có : 

15x = -10y

=> 3.x = -2.y => x/-2 = y/3 [1]

-10y = 6.z

=> -5.y = 3.z => y/3 = z/-5 [2]

Từ [1] và [2] => x/-2 = y/3 = z/-5

Đặt x/-2= y/3 = z/-5 = k

=> x= -2k ; y= 3k  ; z= -5k

=> xyz = 30. k^3 = 30000 => k^3 = 1000 => k = 10

=> x= -20 ; y = 30 ; z= -50

Vậy x= -20 ; y= 30 ; z= -50

15x = -10y = 6z

<=> \(\frac{15x}{30}=\frac{-10y}{30}=\frac{6z}{30}\) 

<=> \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}\)

Đặt \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}=k\Rightarrow\hept{\begin{cases}x=2k\\y=-3k\\z=5k\end{cases}}\)

Ta có: xyz = -30000

=> 2k.(-3k).5k = -30000

=> -30k³ = -30000

=> k³ = 1000

=> k = 10

=> x = 20, y = -30, z = 50

Vì  15x = -10y = 6z => \(\frac{15x}{30}=\frac{-10y}{30}=\frac{6z}{30}\)  => \(\frac{x}{2}=\frac{-y}{3}=\frac{z}{5}\)

Đặt : \(\frac{x}{2}=\frac{-y}{3}=\frac{z}{5}=k\), ta có : x = 2k ; y = (-3).k ; x = 5k

=> x.y.z = 2   .k. ( -3 ). k.5.k = -30.k³ = -30000

=> k³ = 1000 => k = 10 => x = 10. 2 = 20

                                     => y = 10. ( - 3 ) = -30

                                      => z = 10.5 = 50

Ta có : 15x = 6z

=> x = 6/15z

-10y = 6z

=>  y= -3/5z

=> xyz = -30000

<=> (6/15z) . (-3/5z) . z = -30000

<=> z^3 .( -6/25) = -30000

<=> z^3       = 125000

<=> z   = 50

=> y = -30

=> x = 20

20 k mk nhe !

\(15x=10y=6z\)

\(\Leftrightarrow\)\(\frac{15x}{30}=\frac{10y}{30}=\frac{6z}{30}\)

\(\Leftrightarrow\)\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\)

Đặt \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\)\(\Rightarrow\)\(\hept{\begin{cases}x=2k\\y=3k\\z=5k\end{cases}}\)

Suy ra \(xyz=-1920\)\(\Leftrightarrow\)\(2k.3k.5k=-1920\)

\(\Leftrightarrow\)\(30k=-1920\)

\(\Leftrightarrow\)\(k=\frac{-1920}{30}\)

\(\Leftrightarrow\)\(k=-64\)

Do đó : 

\(x=2k=2.\left(-64\right)=-128\)

\(y=3k=3.\left(-64\right)=-192\)

\(z=5k=5.\left(-64\right)=-320\)

Vậy \(x=-128\)\(;\)\(y=-192\) và \(z=-320\)

Chúc bạn học tốt ~ 

Cảm ơn bạn nhiều nha !

Chúc bạn học tốt !

Bạn kết bạn với mình nhé !

2) \(\frac{x}{5}\)=\(\frac{9}{23}\)và xy=460

\(15x=-10y\) => \(\frac{x}{-10}=\frac{y}{15}\) => \(\frac{x}{-2}=\frac{y}{3}\)

 \(-10y=6z\) => \(\frac{y}{6}=\frac{z}{-10}\) => \(\frac{y}{3}=\frac{z}{-5}\)

=> \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}\)

=> \(\left(\frac{x}{2}\right)^3=\left(\frac{y}{-3}\right)^3=\left(\frac{z}{5}\right)^3=\frac{xyz}{2.-3.5}=\frac{-30000}{-30}=1000\)

=> x = 20

y = -30

z = 50

Chúc bạn làm bài tốt

\(15x=-10y=6z\Rightarrow\frac{15x}{30}=\frac{-10y}{30}=\frac{6z}{30}\)

\(\Rightarrow\)\(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}\)

Đặt   \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}=n\)

\(\Rightarrow x=2n,y=-3n,z=5n\)

\(\Rightarrow xyz=2n.-3n.5n\)

\(=-30n^3=-30000\Rightarrow n^3=-1000=-10^3\)

\(\Rightarrow n=-10\)

\(15x=10y=6z\)

\(\Rightarrow\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)

Áp dụng t/c dtsbn:

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{x+y+z}{2+3+5}=\dfrac{20}{10}=2\)

\(\Rightarrow\left\{{}\begin{matrix}x=2.2=4\\y=2.3=6\\z=2.5=10\end{matrix}\right.\)

\(15x=-10y=6z\Leftrightarrow\frac{15x}{30}=\frac{-10y}{30}=\frac{6z}{30}\)

\(\Leftrightarrow\frac{x}{2}=\frac{-y}{3}=\frac{1}{5}\)

Đặt \(\frac{x}{2}=\frac{-y}{3}=\frac{1}{5}=k\)

\(\Rightarrow x=2k;y=-3k;z=5k\)

\(\Rightarrow xyz=-30000\Leftrightarrow2k\cdot\left(-3\right)k\cdot5k=-30000\)

\(\Leftrightarrow-30k^3=-30000\)

\(\Leftrightarrow k^3=1000\)\(\Leftrightarrow k=10\)

\(\Rightarrow\begin{cases}x=2k=2\cdot10=20\\y=\left(-3\right)k=-3\cdot10=-30\\z=5k=5\cdot10=50\end{cases}\)

Ta có: 15x = -10y = 6z

\(=\frac{x}{\frac{1}{15}}=\frac{y}{\frac{-1}{10}}=\frac{z}{\frac{1}{6}}\)

\(\Rightarrow\left(\frac{x}{\frac{1}{15}}\right)^3=\left(\frac{y}{\frac{-1}{10}}\right)^3=\left(\frac{z}{\frac{1}{6}}\right)^3=\frac{x}{\frac{1}{15}}.\frac{y}{\frac{-1}{10}}.\frac{z}{\frac{1}{6}}\)

\(=\frac{x^3}{\frac{1}{15^3}}=\frac{y^3}{\frac{-1}{10^3}}=\frac{z^3}{\frac{1}{6^3}}=\frac{-30000}{\frac{-1}{900}}=300\)

\(\Rightarrow\begin{cases}x^3=300^3.\frac{1}{15^3}=20^3\\y^3=300^3.\frac{-1}{10^3}=-30^3\\z^3=300^3.\frac{1}{6^3}=50^3\end{cases}\)\(\Rightarrow\begin{cases}x=20\\y=-30\\z=50\end{cases}\)

Vậy x = 20; y = -30; z = 50

Ta có: 15x = -10y = 6z

\(=\frac{x}{\frac{1}{15}}=\frac{y}{\frac{-1}{10}}=\frac{z}{\frac{1}{6}}\)

\(\Rightarrow\left(\frac{x}{\frac{1}{15}}\right)^3=\left(\frac{y}{\frac{-1}{10}}\right)^3=\left(\frac{x}{\frac{1}{6}}\right)^3=\frac{x}{\frac{1}{15}}.\frac{y}{\frac{-1}{10}}.\frac{z}{\frac{1}{6}}\)

\(=\frac{x^3}{\frac{1}{15^3}}=\frac{y^3}{\frac{-1}{10^3}}=\frac{z^3}{\frac{1}{6^3}}=\frac{-30000}{\frac{1}{15}.\frac{-1}{10}.\frac{1}{6}}=\frac{-30000}{\frac{1}{900}}=-30000.900=-27000000=\left(-300\right)^3\)

\(\Rightarrow\begin{cases}x^3=\left(-300\right)^3.\frac{1}{15^3}=\left(-20\right)^3\\y^3=\left(-300\right)^3.\frac{-1}{10^3}=30^3\\z=\left(-300\right)^3.\frac{1}{6^3}=\left(-50\right)^3\end{cases}\)\(\Rightarrow\begin{cases}x=-20\\y=30\\z=-50\end{cases}\)

Vậy \(x=-20;y=30;z=-50\)

\(15x=-10y=6z\)  =>  \(\frac{x}{2}=\frac{y}{-3}=\frac{z}{5}=k\)

=>  \(x=2k;\) \(y=-3k;\)\(z=5k\)

Ta có: \(x.y.z=-30000\)

<=> \(2k.\left(-3k\right).5k=-30000\)

<=> \(-30k^3=30000\)

<=> \(k^3=1000\)

<=> \(k=10\)

suy ra: \(x=20;\)\(y=-30\)\(z=50\)