  This paper shows the complementary roles of mathematical and engineering
points of view when dealing with truss analysis problems involving systems of
linear equations and inequalities. After the compatibility condition and the
mathematical structure of the general solution of a system of linear equations
is discussed, the truss analysis problem is used to illustrate its mathematical
and engineering multiple aspects, including an analysis of the compatibility
conditions and a physical interpretation of the general solution, and the
generators of the resulting affine space. Next, the compatibility and the
mathematical structure of the general solution of linear systems of
inequalities are analyzed and the truss analysis problem revisited adding some
inequality constraints, and discussing how they affect the resulting general
solution and many other aspects of it. Finally, some conclusions are drawn.
