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pulley system with one mass and apparently independent forces?

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So at my gym, there's a cable machine that works like this: You pull on one cable and you lift x mass using y force. You pull the other and find the same thing. If, however, you pull on both, you're still only lifting x mass (you can see the weights) yet somehow each cable is still requiring y force. I actually held ~80lbs in both arms, and then released one. Intuitively, I should then be resisting 160lbs with one arm, which aside from being well beyond my ability, should have at least been noticeable. Yet I found no noticeable difference at all.
I was just wondering how a system could be set up to allow for this kind of thing.

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