1) \(\frac{x}{2}=\frac{y}{3}=\frac{z}{7}=\frac{2x-4y+3z}{2.2-4.3+3.7}=\frac{-39}{13}=-3\)

\(\Leftrightarrow\hept{\begin{cases}x=-3.2=-6\\y=-3.3=-9\\z=-3.7=-21\end{cases}}\)

2) \(9x=10y\Leftrightarrow\frac{x}{10}=\frac{y}{9},4y=3z\Leftrightarrow\frac{y}{9}=\frac{z}{12}\)

suy ra \(\frac{x}{10}=\frac{y}{9}=\frac{z}{12}=\frac{x-y+z}{10-9+12}=\frac{78}{13}=6\)

\(\Leftrightarrow\hept{\begin{cases}x=6.10=60\\y=6.9=54\\z=6.12=72\end{cases}}\)

3) \(3x=4y=6z\Leftrightarrow\frac{x}{4}=\frac{y}{3}=\frac{z}{2}=\frac{x-y+z}{4-3+2}=\frac{-9}{3}=-3\)

\(\Leftrightarrow\hept{\begin{cases}x=-3.4=-12\\y=-3.3=-9\\z=-3.2=-6\end{cases}}\)

Ta có: 2x=3y

nên \(\dfrac{x}{3}=\dfrac{y}{2}\)

hay \(\dfrac{x}{9}=\dfrac{y}{6}\left(1\right)\)

Ta có: 4y=6z

nên \(\dfrac{y}{6}=\dfrac{z}{4}\left(2\right)\)

Từ (1) và (2) suy ra \(\dfrac{x}{9}=\dfrac{y}{6}=\dfrac{z}{4}\)

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

\(\dfrac{x}{9}=\dfrac{y}{6}=\dfrac{z}{4}=\dfrac{x+2y-3z}{9+2\cdot6-3\cdot4}=\dfrac{9}{9}=1\)

Do đó: x=9; y=6; z=4

\(a,4x=5y\:\Rightarrow\frac{x}{5}=\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{12}\)

\(4y=6z\Rightarrow\frac{y}{6}=\frac{z}{4}\Rightarrow\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{x}{15}=\frac{2y}{24}=\frac{3z}{24}\)

\(\Rightarrow\frac{x-2y+3z}{15-24+24}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{5}{15}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\frac{1}{3}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{1}{3}\cdot15=5\\y=\frac{1}{3}\cdot12=4\\z=\frac{1}{3}\cdot8=\frac{8}{3}\end{cases}}\)

mọi người giúp mk câu b, c, d còn lại nha

Ta có: 3x = 4y => \(\frac{x}{4}=\frac{y}{3}\) => \(\frac{x}{8}=\frac{y}{6}\)

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

=> \(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}\)

Áp dụng t/c của dãy tỉ số bằng nhau, ta có: 

       \(\frac{x}{8}=\frac{y}{6}=\frac{z}{5}=\frac{x+y-z}{8+6-5}=\frac{18}{9}=2\)

=> \(\hept{\begin{cases}\frac{x}{8}=2\\\frac{y}{6}=2\\\frac{z}{5}=2\end{cases}}\) => \(\hept{\begin{cases}x=2.8=16\\y=2.6=12\\z=2.5=10\end{cases}}\)

Vậy ....

Ta có: \(\frac{x}{-3}=\frac{y}{7}\Leftrightarrow\frac{x}{6}=\frac{y}{-14}\) mà \(\frac{y}{-14}=\frac{z}{5}\)

=> \(\frac{x}{6}=\frac{y}{-14}=\frac{z}{5}\)

Áp dụng t/c dãy tỉ số bằng nhau ta có: 

\(\frac{x}{6}=\frac{y}{-14}=\frac{z}{5}=\frac{2x+4y-6z}{12-56-30}=-\frac{15}{74}\)

\(\Rightarrow\hept{\begin{cases}x=-\frac{15}{74}\cdot6=-\frac{45}{37}\\y=-\frac{15}{74}\cdot\left(-14\right)=\frac{105}{37}\\z=-\frac{15}{74}\cdot-\frac{75}{74}\end{cases}}\)