\[ \text{Consider the system} \begin{aligned} x + 2y + z &= 4,\\ 2x + 4y + 2z &= 8,\\ 3x + 6y + 3z &= 10. \end{aligned} \] \[ \text{Observe that the second equation is }2\text{ times the first: }(2x+4y+2z)=2(x+2y+z)=8. \] \[ \text{If the third were consistent with the first, it would be }3(x+2y+z)=3\cdot 4=12, \] \[ \text{but the third equation has right-hand side }10\neq 12, \] \[ \text{so the three equations are inconsistent.} \] \[ \text{Augmented matrix row-reduction (illustration):} \] \[ \left[\begin{array}{ccc|c} 1 & 2 & 1 & 4\\[4pt] 2 & 4 & 2 & 8\\[4pt] 3 & 6 & 3 & 10 \end{array}\right] \overset{R_2\leftarrow R_2-2R_1}{\longrightarrow} \overset{R_3\leftarrow R_3-3R_1}{\longrightarrow} \left[\begin{array}{ccc|c} 1 & 2 & 1 & 4\\[4pt] 0 & 0 & 0 & 0\\[4pt] 0 & 0 & 0 & -2 \end{array}\right]. \] The last row $[0\;0\;0\;|\;-2]$ is a contradiction, so the system has no solution. \[ \boxed{\text{Option 2: no solution}} \]