Dear Chathranee,

maybe those papers will be helpful for you.

Greetings, Tadeusz

So many methods are available, specially  in Algebra books

Numerical analysis by Gerald a best book.

Following links, paper link may be helpful for you ....

http://www.mathplanet.com/education/algebra-1/systems-of-linear-equations-and-inequalities/the-elimination-method-for-solving-linear-systems

http://www.scirp.org/journal/PaperInformation.aspx?PaperID=22660

There are many methods...see link

http://ins.sjtu.edu.cn/people/mtang/textbook.pdf

Non-linear systems usually require updating of the matrices involved with each iteration, hence, most of the better methods, like LU decomposition, are not as efficient, because the matrix changes with each iterate of calculation.

Thank you all for your answers. They are really helpful to me. 

I hope this paper to be helpful.

Best Regards.

A New Iterative Solution Method for Solving Multiple Linear Systems ( http://www.scirp.org/journal/PaperDownload.aspx?paperID=22660 )