The maximum resolution supported by my graphic card is sadly 1366x768 . After getting used to my work computer with the resolution 1920x1080, using my personal computer became very painful. I was wondering whether there were ways to cheat and regardless increase the resolution.
Im sorry but your only option is to install a better graphics card. When buying a new graphics card, make sure that the graphics card is compatible with the computer. Have a sales rep recommend one for you. For future reference when asking questions, any problem involving physical hardware can only be solved by repairing or replacing hardware.
You won't cheat pixels, but if you want to cheat resolution, you might try this..
Say your native resolution is 1600x900, and you can set windows resolution to even 2560x1440, as seen here: https://superuser.com/a/533751/187737