Equation of plane containing the line $2\mathrm{x}+\mathrm{z}-4=0, 2\mathrm{y}+\mathrm{z}=0$ and passing through the point $\left(2,1,-1\right)$ is

$\begin{array}{rcl}{\mathrm{\pi }}_1+{\mathrm{\lambda }}_2 & =& 0\\ (2\mathrm{x}+\mathrm{z}-4)+\mathrm{\lambda }(2\mathrm{y}+\mathrm{z})& =& 0\end{array}$

it is passing through (2, 1, -1)

$\begin{array}{rcl}(4-1-4)+\mathrm{\lambda }(2-1)& =& 0\\ -1+\mathrm{\lambda }& =& 0\\ \mathrm{\lambda }& =& 1\\ 2\mathrm{x}+\mathrm{z}-4+2\mathrm{y}+\mathrm{z}& =& 0\\ 2\mathrm{x}+2\mathrm{y}+2\mathrm{z}-4& =& 0\\ \mathrm{x}+\mathrm{y}+\mathrm{z}-2& =& 0\end{array}$