Series connection of transmission lines described by telegrapher's equations
Is it possible to obtain an equivalent aggregated model in the form of
telegrapher's equation via linear combination of the two systems?

No, it's not possible.
Reason: at the junction of two real but different transmission lines, there will be a reflection coming back to the source due to the disparity of the two characteristic impedances and, this cannot be adequately modelled by a single &quot;new and modified&quot; transmission line because it will not naturally produce reflections at some distance along its length.