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

(1)+(2)−(3)⇒(x+2y+z)+(2x+3y+z)−(3x+5y+2z)=3+3=1 ⇒0=5 which is an absurd result.Thus, the system of equations has no solution.