When poet William Blake wrote of "dark satanic mills", he couldn't have been looking at a steel mill because there were none in 1804. Nevertheless, when I visit a steel mill, Blake's phrase always comes to mind. With the heat and the pounding noise, the dust and smoke, and the red glow against the night sky, it's hard not to see these places as infernal. And yet the process of making steel also produces some of the most hauntingly beautiful images found anywhere in the world of industry.
While the client has some knowledge of his symptoms, he may not understand the real causes of them, and it is foolish to try to cure the symptoms only. Thus while the systems engineers must listen to the client, they should also try to extract from the client a deeper understanding of the phenomena. Therefore, part of the job of a systems engineer is to define, in a deeper sense, what the problem is and to pass from the symptoms to the causes.
Just as there is no definite system within which the solution is to be found, and the boundaries of the problem are elastic and tend to expand with each round of solution, so too there is often no final solution, yet each cycle of input and solution is worth the effort. A solution which does not prepare for the next round with some increased insight is hardly a solution at all.
I suppose the heart of systems engineering is the acceptance that there is neither a definite fixed problem nor a final solution, rather evolution is the natural state of affairs. This is, of course, not what you learn in school, where you are given definite problems which have definite solutions.