Systems therapists are interested in helping a family, couple, community, school system, country etc. to function with dynamics and structures which 
best support the well being and potential of the pieces which make up the system. Systems theory taken to a radical (and dichotomous) position would state that problems do not exist within individuals; instead, ‘problems’ are the result of a systems inability to effectively attend to the needs of the individuals in the system… labeling a person as the problem is a symptom of the systems inability to augment its strengths and to adapt in ways that facilitate dynamics and structures which are best suited to the ‘pieces’ (people) in the system.
Systemic theories tend to be strength based… this means that the intervention focusing on creating solutions and augmenting strengths as opposed to overly focusing on the removal of a problem. The idea again is that the problem (symptom) will naturally go away as the system increases effectiveness.
Mechanic metaphor = let’s say you have a car and a piece keeps on breaking… how about the water pump… the individual perspective (or western, or medical) focuses on the dysfunctional piece (the water pump)… the intervention will focus on fixing the broken piece. The systemic intervention would focus all the pieces that could be effecting the water pump… the water pump would not be the problem it would be the dynamics of the entire system which needed adjustment.
“How was the system dysfunctioning in a way which was causing a piece to break?” or “how could the interaction between all the pieces be adjusted so that the pieces could function most effectively?”
I am personally a ‘both and’ kinda guy… I intervene on a systems and on an individual level. I would fix the structural integrity of the water pump and intervene to ensure the system was not overworking the water pump.