Can I download to my 32 bit XP desktop and my 64 bit W7 laptop without having to buy more than a single license?
Just to add on, You didn't mention which Elements 10 , Is it Premiere elements or Photoshop Elements
However when you are installing it on Win XP then please check the tech specs.
Because Photoshop elements need SP3 and Premiere elements need SP2 as minimum requirement , check
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