The supporting system of teaching is :

In the context of education, supporting systems of teaching are resources and facilities that aid the teaching-learning process. These systems provide additional opportunities for exploration, research, practice, and reinforcement of concepts taught in the classroom. 

Key Points

•  Laboratories offer students a space to engage in experiments and practical applications, especially in science and technology subjects, making theoretical concepts more understandable.
• Libraries provide access to a vast range of books, journals, and digital resources, supporting both teachers and students in extending their learning.
• When combined, these two systems offer comprehensive academic support.
• They complement classroom teaching by enabling both experiential and research-based learning. 

Hence, the correct answer is both Laboratory and Library.