  We present a new technique for constructing solutions of quasilinear systems
of first-order partial differential equations, in particular inhomogeneous
ones. A generalization of the Riemann invariants method to the case of
inhomogeneous hyperbolic and elliptic systems is formulated. The algebraization
of these systems enables us to construct certain classes of solutions for which
the matrix of derivatives of the unknown functions is expressible in terms of
special orthogonal matrices. These solutions can be interpreted as nonlinear
superpositions of $k$ waves (or $k$ modes) in the case of hyperbolic (or
elliptic) systems, respectively. Theoretical considerations are illustrated by
several examples of inhomogeneous hydrodynamic-type equations which allow us to
construct solitonlike solutions (bump and kinks) and multiwave (mode)
solutions.
