Most important is to check GPU requirement for OBS (DirectX12??) and your system
Realize that video encoding is one of the more demanding workloads for a consumer computer
I'm not a gamer, so no idea exactly .... but based on my experience with a simple non-gaming stream from USB webcam on a gaming laptop with an i5-6300HQ (4c/4t) Fall 2015 release, Nvidia GeForce GTX 960M graphics card and 8GB RAM failed miserably... I wouldn't have high hopes
- an i3 is a 4 generations old low-end Intel chip (2c/4t), and the U meaning laptop, low power. You don't mention RAM nor GPU, but with a low-end CPU (for video encoding) I'm suspecting your don't have a decent nVidia GPU in same machine.
So... just a guess on my part... highly unlikely at decent frame rates and resolutions
As such, I highly doubt you could stream different resolutions to YT and FB with such a machine (as it would have to encode each separately)
Could you pull off a single stream to restream.io (and let them split stream to YT &FB)... at 1080p/30fps .... maybe... but, were you thinking of any overlays, Picture-in-Picture, etc? all of that would add CPU load. The beauty of free software like OBS is that you can try without cost and see what you can accomplish. What you spend in time learning how to use and optimize OBS for your use case can then be applied even if you need to buy a new machine
For gamers to respond, please reply with what you are looking to accomplish in terms of a stream (framerate/resolution, any screen content other than the single video out from the console? etc