If you are a user on your system that has sudo privileges to run commands as root, just pre-pend sudo to the command.
system("sudo yum install some-package");
If you want anybody to be able to do it, then you have to be administrator on your system, change the owner of the file to be root, and modify the permissions of your executable to run as root. By doing so, you do not need to modify your system() command string with sudo.
chmod +s my_program
chown root my_program
Realize that doing this may open you up to security problems, unless you have proven that your program has no security issues.
The file-system may be such to disallow you from setting the setuid bit on your program. If you need more information along these lines, you should consult SuperUser.