I installed linux on my computer and downloaded CS:S from steam but when i try to run it it just shows a black screen and closes by itself. any responses are helpful.
Not a lot to go on there. Which OS are you running (Which GNU/Linux distro since you have steam on it), what kind of PC is it, what graphics drivers are you using.
Most common thing that goes wrong with steam: no X11 32-bit libraries on a 64-bit GNU/Linux install. Steam needs the 32-bit libraries since it's a 32-bit application, even on a 64-bit install.
i have ubuntu 12.10 its a 32bit and i have no graphics driver installed pretty new so dont know much. i have an amd phenom ii cpu and a xfx r7850 gpu