\(\hept{\begin{cases}\frac{x-3}{2}=\frac{y-4}{3}=\frac{z+5}{4}\\x-3y+z=8\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x-3}{2}=\frac{3\left(y-4\right)}{3\cdot3}=\frac{z+5}{4}\\x-3y+z=8\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x-3}{2}=\frac{3y-12}{9}=\frac{z+5}{4}\\x-3y+z=8\end{cases}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(...=\frac{x-3-\left(3y-12\right)+z+5}{2-9+4}=\frac{x-3-3y+12+z+5}{2-9+4}=\frac{\left(x-3y+z\right)-3+12+5}{2-9+4}=\frac{8-3+12+5}{2-9+4}=-\frac{22}{3}\)
\(\frac{x-3}{2}=-\frac{22}{3}\Rightarrow x-3=-\frac{44}{3}\Rightarrow x=-\frac{35}{3}\)
\(\frac{y-4}{3}=-\frac{22}{3}\Rightarrow y-4=-22\Rightarrow y=-18\)
\(\frac{z+5}{4}=-\frac{22}{3}\Rightarrow z+5=-\frac{88}{3}\Rightarrow z=-\frac{103}{3}\)
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