If the system of equations
Question:

If the system of equations

$k x+y+2 z=1$

$3 x-y-2 z=2$

$-2 x-2 y-4 z=3$

has infinitely many solutions, then $\mathrm{k}$ is equal to_______.

Solution:

We observe $5 \mathrm{P}_{2}-\mathrm{P}_{1}=3 \mathrm{P}_{3}$

So, $15-\mathrm{K}=-6$

$\Rightarrow \mathrm{K}=21$