Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{5}.\)
=> \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{5}\) và \(x+y+z=11.\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{5}=\frac{x-1+y+3+z-5}{2+4+5}=\frac{\left(x+y+z\right)-\left(1-3+5\right)}{11}=\frac{11-3}{11}=\frac{8}{11}.\)
\(\Rightarrow\left\{{}\begin{matrix}\frac{x-1}{2}=\frac{8}{11}\Rightarrow x-1=\frac{16}{11}\Rightarrow x=\frac{27}{11}\\\frac{y+3}{4}=\frac{8}{11}\Rightarrow y+3=\frac{32}{11}\Rightarrow y=-\frac{1}{11}\\\frac{z-5}{5}=\frac{8}{11}\Rightarrow z-5=\frac{40}{11}\Rightarrow z=\frac{95}{11}\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)=\left(\frac{27}{11};-\frac{1}{11};\frac{95}{11}\right).\)
Chúc bạn học tốt!