Ta có : \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\Rightarrow\frac{x-1}{2}=\frac{2\left(y-2\right)}{6}=\frac{3\left(x-3\right)}{12}\)

hay 

\(\frac{x-1}{2}=\frac{2y-4}{6}=\frac{3z-9}{12}\) và \(x-2y+3z=-10\)

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

\(\frac{x-1}{2}=\frac{2y-4}{6}=\frac{3z-9}{12}=\frac{x-1-\left(2y-4\right)+\left(3z-9\right)}{2-6+12}=\frac{x-1-2y-4+3z-9}{8}\)

\(=\frac{\left(x-2y+3z\right)-\left(9+1-4\right)}{8}=\frac{-10-6}{8}=-\frac{16}{8}=-2\)

\(\Leftrightarrow\begin{cases}x-1=-2.2=-4\Rightarrow x=-4+1=-3\\y-2=-2.3=-6\Rightarrow y=-6+2=-4\\z-3=-2.4=-8\Rightarrow z=-8+3=-5\end{cases}\)

Khi đó : \(x+y+z=\left(-3\right)+\left(-4\right)+\left(-5\right)=-12\)

Ap dung tinh chat day ti so bang nhau ta co : 

x-1/2=y-2/3=z-3/4=(x-1)-2(y-2)+3(z-3)/2-2.3+3.4=x-1+2y+4+3z-9/2-6+12=(x-2y+3z)+(-1+4-9)=-10-6/8=-2

Suy ra : x-1/2=-2=>x-1=-4=>x=-3

y-2/3=-2=>y-2=-6=>y=-4

z-3/4=-2=>z-3=-8=>z=-5

nho lik e nhe

\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)vậy hả

đặt \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=k\)(k\(\in\)Z)

=>x-1=2k=>x=2k+1

y-2=3k=>y=3k+2

z-3=4k=>z=4k+3

thay x=2k+1;y=3k+2;z=4k+3 vào x-2y+3z=-10 ta được :

2k+1-2(3k+2)+3(4k+3)=-10

2k+1-6k-4+12k+9=-10

8k+6=-10

8k=-10-6

8k=-16

k=-2

=>x=2k+1=2.(-2)+1=-4+1=-3

=>y=3k+2=3.(-2)+2=-6+2=-4

=>z=4k+3=4.(-2)+3=-8+3=-5

vậy x=-3;y=-4;z=-5

đặt x−12 =y−23 =z−34 =k(k∈Z)

=>x-1=2k=>x=2k+1

y-2=3k=>y=3k+2

z-3=4k=>z=4k+3

thay x=2k+1;y=3k+2;z=4k+3 vào x-2y+3z=-10 ta được :

2k+1-2(3k+2)+3(4k+3)=-10

2k+1-6k-4+12k+9=-10

8k+6=-10

8k=-10-6

8k=-16

k=-2

=>x=2k+1=2.(-2)+1=-4+1=-3

=>y=3k+2=3.(-2)+2=-6+2=-4

=>z=4k+3=4.(-2)+3=-8+3=-5

vậy x=-3;y=-4;z=-5

ap dung tinh chat day ti so bang nhau ta co : 

x-1/2=y-2/3=z-3/4=(x-1)-2.(y-2)+3.(z-3)/2-2.3+3.4

=x-1-2y+4+3z-9/2-6+12 = (x-2y+3z)+(-1+4-9)/8

= 14-6/8 

=1

Suy ra :

x-1/2=1=>x-1=2=>x=3

y-2/3=1=>y-2=3=>y=5

z-3/4=1=>z-3=4=>z=7 

nho lik e nhe thanks