Why can you solve system of lenses combining the effects?

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physics user1
In solving a system of lenses you have to work like the second lens doesn't exist and then use the image formed by the first lens and work like the first doesn't exist, how can i demonstrate that doing so is correct?
Why is that correct?
The path that the rays make is different as is is if the rays were coming from the image formed from the first lens...
Whst is the first image was virtual, and the second happened to be real, how is this possible?
 
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If I understand your question correctly, the image from the first lens is not really "virtual". It really is the image that is projected onto the second lens of a combined system. So the result of the combined system is the result of the second lens operating on the image from the first lens.