  We use semiclassical Boltzmann transport theory to analytically study the
electronic contribution to the linear thermoelectric response of anisotropic
two-dimensional materials subjected to a perpendicular magnetic field.
Conventional methods, such as the relaxation-time approximation within the
Boltzmann formalism, often yield qualitatively incorrect results when applied
to anisotropic mediums. On the other hand, the vector mean free path provides
exact solutions for the linearized Boltzmann transport equation, and in
principle, we can systematically evaluate it to any desired order in the
external magnetic field. After laying out the general formalism of the
magneto-thermoelectric responses of anisotropic systems based on the vector
mean free path approach, we study the longitudinal and Hall charge
conductivities, as well as the Seebeck and Nernst coefficients of two
representative anisotropic two-dimensional electronic systems: a semi-Dirac
semimetal and a two-dimensional system of tilted massless Dirac fermions.
