How to wire a low voltage light system to a traditional overhead light fixture?

I would like to install low voltage lights under the kitchen cabinets of my small kitchen. Instead of plugging the low voltage lights into the already limited number of outlets, I would like to wire the low voltage system to the overhead light fixture. I could then run the low voltage lights to either side of the... show more I would like to install low voltage lights under the kitchen cabinets of my small kitchen. Instead of plugging the low voltage lights into the already limited number of outlets, I would like to wire the low voltage system to the overhead light fixture. I could then run the low voltage lights to either side of the kitchen and those initial wires would run across the attic, above the ceiling The tranfsformer would be in the attic too. the same light switches would turn both the main light and the low voltage lights too. Do you see any problems with this proposed idea? If so, can you recommend an alternative. Thanks.
Update: The ceiling light fixture is on a 15 amp breaker. I do not think that this breaker is controlling the electricity on a lot of lights or appliances. The current ceiling light fixture itself has 2 cfl bulbs. will just adding the the low voltage lights to this configuration cause the current switches that are in... show more The ceiling light fixture is on a 15 amp breaker. I do not think that this breaker is controlling the electricity on a lot of lights or appliances. The current ceiling light fixture itself has 2 cfl bulbs. will just adding the the low voltage lights to this configuration cause the current switches that are in place to shut off both the ceiling light fixture and the low voltage lights?
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