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, $15-\mathrm{K}=-6$
$\Rightarrow \mathrm{K}=21$