If you open too many webpages in a same computer of the same network will it slow down the other people's internet using the same network?

Technically, no.

It does depend what you are doing on each of those webpages. If each page is downloading some kind of content, e.g. files, pictures, mp3s, streaming music or video, then it could possibly impact network performance. This applies not just to web browsing but to any application accessing the internet. So, if you have iTunes downloading an album, Limewire or Gnucleus downloading mp3s, watching a YouTube video, listening to a ShoutCast, and streaming radio from IM, then you'd surely be using up bandwidth. This is especially true if you are sharing a slow DSL link to the Internet.

Having several pages open with static content, i.e. reading blogs or news, browsing Facebook, etc. will usually not impact network performance. Do keep in mind that having too many web browser Windows or tabs open impacts your PC's performance by taking up CPU and memory resources.