[tex]\it \{x,\ y,\ z\}\ i.\ p.\ \{4,\ 3,\ 2\}\ \Rightarrow 4x=3y=2z\ \ \ \ \ (1)\\ \\ 4x+6y+8z=42|_{:2} \Rightarrow 2x+3y+4z=21\ \ \ \ \ (2)\\ \\ (1) \Rightarrow \begin{cases}\it 3y=4x\\ \\ \it 2z=4x|_{\cdot2} \Rightarrow 4z=8x\end{cases}\ \ \ \ \ \ (3)\\ \\ \\ (2),\ (3) \Rightarrow 2x+4x+8x=21 \Rightarrow 14x=21 \Rightarrow x=\dfrac{\ 21^{(7}}{14} \Rightarrow x=\dfrac{3}{2}=1,5\ \ \ \ \ \ (4)[/tex]
[tex]\it (3), (4) \Rightarrow \begin{cases}\it 3y = 4\ \cdot 1,5 \Rightarrow 3y=6|_{:3} \Rightarrow y=2\\ \\ \it 4z=8 \cdot1,5 \Rightarrow 4z = 12|_{:4} \Rightarrow z=3\end{cases}[/tex]
