If your backpack is compact enough and the gear within it can be safely mashed, you could just bungee your backpack on top of your other gear on your rack. I've done this a few times and it works no problem, see pic...
It's a good idea to cross the bungee chords through the straps to secure it a little better.
On the other hand I've tried to carry a laptop and other equipment in a larger backpack loaded to about 15 lbs on a 25 mile commute and it just about killed my neck.
Riding is better without a backpack of course, but if it's your only option, under 10 lbs on your back isn't bad at all, but any more than that over a decent distance and you will be in misery.