^ Yep that will do it. If you have access to any other PC/Laptop you can easily make on yourself. No extra skill needed just follow the windows directions.
Windows 7 was great, I used it since launch day until the first year of 8.1. I am not preaching here it's totally up to you of course. But in addition to less security (not as terrible as makeout) things like this are more problematic. For example, your friend or anyone who could make one for you easily probably has ten. As far as I know a Win 7 recovery disk will not work for W10.
Depending on age and how much longer you will use current W7 PC I think it a good idea to really give W10 consideration. Whole image can be downloaded from MS, then you need a code.
I have several PCs and have re-imaged plenty. But I have not needed a new key for about 10 years. The same key has worked without uninstillation on original PC many times!! I was amazed at first. Free full edition windows with an old key without uninstalling the original PCs OS. I never used the cheaper OEM keys so can't comment about that, but for the cost of two full (non OEM) older (one is vista, one is W7). I have used them without any uninstallation well over 10 times on new builds, or major changes. Crazy, but Great!!
The only time it took a while was my current gaming rig - it activated on the third try old key. That one has been used over 5 times on new builds now. Basically it's free full licence for totally free. It may be as my original licences which were bought with W7 and Vista are full non OEM editions which allow moving to another PC - thing is I didnt "move" any. One key has worked 4 times now while keeping original PC upgraded and running. The other over 5 times. NO unistallation. So I am saying this because:
--Your W7 key may work. The only unknown by me is that I have never used the cheap OEM keys. It's just a guess that this is the reason - full licence vs one time one PC OEM?? Worth a try anyhow.
I heard that MS were not at all strict about single home users, as opposed to offices they are very lose about checking key if it's a none OEM one.
So in addition to the posters solution above mine, you could upgrade for free? Of course other things such as personal files photos etc that are not backed up come into to it, maybe. What I wrote is the outline for reusing a single genuine Windows (non OEM) many times on various newer PCs. I have three currently all using the same old W7 key!!