Can any circuit with multiple voltage sources be solved without superposition?

[CC4]

TL;DR

When, if ever, is it necessary to use the superposition principle in order to solve a circuit?

When, if ever, is it necessary to use the superposition principle in order to solve a circuit?

Can any circuit with multiple independent voltage sources be solved without superposition?

 

[Baluncore]

Welcome to PF.
Superposition can be applied only to linear systems. It cannot be applied to systems that have non-linear resistance, or that generate harmonic distortion.

When, if ever, is it necessary to use the superposition principle in order to solve a circuit?

Can any circuit with multiple independent voltage sources be solved without superposition?

Superposition is implicit in the application of Kirchhoff's current and voltage laws to any circuit where voltages are added in series, or currents merge or separate at a node.

 

[anorlunda]

Matrix methods can solve arbitrarily large circuits. But as @Baluncore said, they implicitly use superposition even if you don't think so.