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In these days, multi-touch technology becomes an important interface in various environments. However, most of multi-touch systems have a characteristic of low applicability so that it is difficult to apply to diverse applications. In this paper, we compare the main three methods of multi-touch systems, and analyze the pros and cons of these systems. By considering applicability and economical efficiency, we propose an infrared LED based system suitable to be used in multi users. To solve coordinate recognition problems in collinear in a 2-dimensional bi-axial coordinate system, we design a 2-dimensional tri-axial coordinate multi-touch system using infrared LEDs. The comparing result between two systems shows that the recognition rate in the biaxial coordinate system is 49 percent and the recognition rate in the tri-axial coordinate system is 99 percent.