Let the number of ivy, nightshade and triffid plants be $i$, $n$ and $t$ respectively.

Then:

$2i+9n+12t=120$ and $i+n+t=20$, where $i>0$; $n>0$; $t>0$.

Multiplying the second equation by 2 and subtracting the new equation from the first:

${\displaystyle 7n+10t=80}$

${\displaystyle \text{Thus}\hspace{1em}7n=10(8-t)}$

Therefore $n$ is a multiple of 10 and since $1\leqq n<20$, $n=10$.

Hence $8-t=7$ and therefore $t=1$.