Final answer:
The trial-and-error method involves making random attempts to find a solution, as opposed to following a systematic and logical approach. It is a common but not time-efficient strategy.
Step-by-step explanation:
The trial-and-error method of solving problems refers to making random attempts until the correct solution is found. This contrasts with a systematic approach, which involves a careful and logical plan of action to solve a problem, often involving the analysis and evaluation of alternative solutions. Trial-and-error is a common strategy despite not being the most time-efficient, and it involves testing various possibilities without necessarily following a specific order or logic, until a satisfactory solution is found.