Are front and rear a/c separate systems?

Someone must have modified it to block off the branch to the rear between the tee and the break. Very common for the lines underneath the vehicle to become leaky then they get converted to front only this way.
 
the dual systems I've seen and worked on share the compressor and condensor and have seperate evaporators, and cold/hot mixing flaps.

If the front works, yours got converted to front only somehow.
 
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