Can you cast a spell with a bow equipped?

Solution 1:

No, when you wield a bow it occupies both hands so you cannot equip a spell at the same time.

Solution 2:

You can't.

The bow is counted as a 'two handed' weapon (but not for skill) so you can't cast a spell while doing it.

This differs from Oblivion as in that game you don't put items in use against 'hands' per se, so you can cast a spell while wielding your bow.