If the system of equations :$(k+1)^3x+(k+2)^3y=(k+3)^3 \;;\;(k+1)x+(k+2)y=k+3\;;\;x+y=1$ is consistent, then the value of $k$ is :

Question

$$\begin {array} {1 1} (1)\;2 & \quad (2)\;-2 \\ (3)\;-1 & \quad (4)\;1 \end {array}$$