The system of linear equations + 2y + 2z = 5 2 + 3y + 5z = 8 4x + +...

∆ = \left|\begin{cases}\lambda & 2 & 2 \\ 2\lambda & 3 & 5 \\ 4 & \lambda & 6\end{cases}\right| = \lambda\left(18 - 5\lambda\right) - 2\left(12\lambda - 20\right) + 2\left(2{\lambda}^{2} - 12\right) = - {\lambda}^{2} - 6\lambda + 16 = \left(\lambda + 8\right)\left(2 - \lambda\right)
$∆ = 0$ for $\lambda = 2$,
{∆}_{1} = \left|\begin{cases}5 & 2 & 2 \\ 8 & 3 & 5 \\ 10 & 2 & 6\end{cases}\right|

${∆}_{1} = 5\left[18 - 10\right] - 2\left[48 - 50\right] + 2\left[16 - 30\right]$

${∆}_{1} = 40 + 4 - 28 \ne 0$
No solution for $\lambda = 2$.