Consider the system of linear equations $x+2y+z=3,2x+3y+z=3$,$3x+5y+2z=1$, then the system has  

$$\begin{gathered} \left(1\right)+\left(2\right)-\left(3\right)\Rightarrow (x+2y+z)+(2x+3y+z)-(3x+5y+2z)=3+3=1 \\ \Rightarrow 0=5 which is an absurd result. \end{gathered}$$

Thus, the system of equations has no solution.