Is it a bad idea to install a book shelf system on drywall?
When attaching anything other than lightweight items to the wall, you want to ensure that you have attached it to the underlying wall studs.
In the case of shelves, except for perhaps very light ornamental shelves, you want to attach the tracks (i.e. the vertical black pieces in your photo) to the studs with screws that are long enough to penetrate the wood enough and strong enough to hold the intended weight.
From looking at the photo it does appear that the 3 tracks are spaced at about the typical width for wall stud spacing.
The best way to find studs is with a commercially made stud finder tool.  These are relatively inexpensive today.  You will also want to ensure that you don't hit and hidden plumbing or electrical wires in the wall, so take a survey of the things on the other side, above and below the wall to try to avoid any damage.