Abstract : Our research work studies teacher's activity, more precisely it analyses practices about the teaching of linear systems and their use in modelling in the class of "troisième" (14 year-old pupils). We adopt a new viewpoint based on the joint use of two of the main theoretical approaches in the field of the French "didactique des mathématiques". Our work shows the complementarity of Chevallard's anthropological approach (viewpoint of the ecology of the system) and Brousseau's theory of didactical situations (viewpoint of the economy of the system) as well as the richness of the articulated use of these two tools in the study of teacher's activity. According to the anthropological approach, the teacher is constrained as a subject of different institutions at different periods. They are what we call the external constraints; we determine them through a study of the evolution of the didactical transposition during the whole 20th century. A questionnaire given to teachers proves that old choices in the transposition are alternative choices taken into account by some teachers in various ways, but yet, their final choices remain conform to the current programme. Within the space of freedom always left to the teacher, subject of an institution, regulations in the didactical relation bring a new type of (internal) constraints to the teacher. Referring to the theory of didactical situations, we analyse these constraints in terms of the economy of the educational system. We analyse the planning and the realisation of a teaching activity introducing the notion of linear systems by a specific teacher. With the use of the didactical notion of variables and 'structuration' of the milieu, we study the teacher's choices, the state of his didactical and mathematical knowledge and the influence of both external and internal constraints on his various decisions in his project and actual teaching.