Yes all models of ps3 support backwards compatibility with ps1 games. The newer models only lost support for ps2 backwards compatibility. Its a common misconception that the ps3 lost all backwards compatibility. Also ps1 games look great on a ps3 running at 1080p.
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You can not play PlayStation 3 games on a PlayStation 1, but you can play PlayStation 1 games on a PlayStation 3. All of the PlayStation consoles are backwards compatible.
NO ... but PS2 games work on PS3 consoles ...
Yes it does work
All PS3 models play PlayStation 1 Games and do so through software emulation.
Yes, you can run Playstation 1 games on a Playstation 3 (PS3), a PS2, and a PS1. You can play them on all the Playstation game systems available, some just work better than others.