I think you are out of luck. The emulator for Windows Mobile 10 and Windows Phone 8.1 uses Hyper-V, which, as far as I know, is not found on Windows 10 basic (you will need to upgrade to pro).
Seems I follow all the troubleshooting on hyper-V. The tests say it is enabled and running, but when launching an emulator it says it is not running. Any ideas?