My laptop model is ASUS A43TA.
The graphic card is excellent but the processor is not very powerful and I feel it could be better as sometimes my laptop become is slow and laggy.
Is it possible to upgrade this system?
It is very rare for mobile processors to be replaceable by the user. They are typically soldered directly to the motherboard to save space and make the system thinner and easier to assemble, typically the assumption is that you buy a system knowing what it can do and what you intend it to do.
Cheap laptops are not suited to playing games properly because they are built for portability and lack more powerful dedicated hardware as you are finding. They are perfectly good for some things but not others.
The graphics seems to suit your needs but you appear to be saying that your system sometimes has problems.
Your processor should be reasonably powerful so it may be that you either have too many programs running sucking up resources like memory. Try uninstalling programs that you do not regularly use, or look into finding out how much memory you have fitted and see if you can upgrade it.
The Asus page for your machine suggests you can fit up to 8GB of memory, that is where I would look first. Potentially you may also be able to replace your hard disk drive with an SSD to increase performance though this is a very expensive upgrade and you may end up increasing the speed of the system at the cost of reducing the amount of storage space.
You are going to have to do some research and find out