Active and passive sentences

I was learning about ACTIVE and PASSIVE sentences and came across this particular example. I know a sentence is said to be Active when the subject of the particular sentence performs the action. For example, "The hunter killed an antelope." In the Passive form it will be "An antelope was killed by the hunter." A sentence becomes Passive when the action is acted upon the subject, and the subject becomes the receiver of the action like the second example I gave.

The book also said that the passive voice is use to express an action in which the actor is unknown, and gave this example "The food had been eaten before we came." What I'm confused about here is that, passive voice contains the preposition "by" which is preceded by the subject, but in this case, there was nothing like that, and I want to know if it's a valid one.

You don't have to specify the agent (the person making the action) in the passive voice unless you want to.

"The food had been eaten before we arrived" suggests that the writer either didn't know who had eaten it or didn't think it was necessary to say who had eaten it. The important point is that the food was gone. "The food had been eaten by the children before we arrived" makes it clear who was to blame for there being no more food.