If the system of linear equations  $x+y+z=5,x+2y+2z=6,x+3y+\lambda z=u$has infinitely many solutions, then the value of $\lambda +u$ is

Augments matrix $=\left[\begin{array}{cccc}1& 1& 1& 5\\ 1& 2& 2& 6\\ 1& 3& \lambda & \mu \end{array}\right]$

                                      $=$$$\begin{gathered} R_2\to R_2-R_1, R_3\to R_3-R_1 \\ \left[\begin{array}{cccc}1& 1& 1& 6\\ 0& 1& 1& 1\\ 0& 2& \lambda -1& \mu -5\end{array}\right] \end{gathered}$$

                                         $=$$$\begin{gathered} R_3\to R_3-2R_1 \\ \left[\begin{array}{cccc}1& 1& 1& 5\\ 0& 1& 1& 1\\ 0& 0& \lambda -3& \mu -7\end{array}\right] \end{gathered}$$

Given system has infinitely many solutions

$\Rightarrow$$\lambda -3=0,u-7=0$

$\Rightarrow \lambda =3,u=7$

$\Rightarrow \lambda +u=3+7=10$