?x?-2?=? can be simplified to ?x?=3?. Divide both sides by ? and we get ?=3.
We can plug that in to the third equation to get the value of Light Bulb.
2LB-3(3)=5, or 2LB-9=5. 2LB=14, therefore LB=7.
Professor Layton wants this Katrielle girl (his daughter, I assume?) home by 10:00, presumably PM.

Which is an accomplishment when you consider Arc System Works exists.