What technology makes possible high-speed Internet access over ordinary residential electrical lines and offers an alternative to DSL or high-speed cable modems?

The answer is "Broadband Over Power Line".

Explanation:

The technology that offers and alternative to DSL and high-speed cable is broadband connection which is a term used for high speed internet access using coaxial or fiber optic cables to reach higher speeds than the other technologies. The technology described in the question is "Broadband Over Power Line" which as the name suggests, makes providing broadband internet connection possible using the power lines in the area.

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