It is possible to configure a router to have a static route for some prefix and to also have that prefix learned by EIGRP. But it is not possible to have both routes in the routing table at the same time.
It might help to consider this question with a small example. Lets assume that you have a static route:
ip route 10.10.0.0 255.255.0.0 serial 0
and to also have EIGRP learn that route over interface Ethernet 0. In this case the routing table would have the static route in the routing table because its administrative distance was better than the AD of EIGRP. If interface serial 0 goes down then the static route is removed from the routing table and the EIGRP route would be used.
It is also possible to configure what is generally called a floating static route. In the example a floating static would be something like:
ip route 10.10.0.0 255.255.0.0 serial 0 200
Now in this case the EIGRP route would be preferred because its AD would be better than the static route (AD = 200). And if the EIGRP route were removed from the routing table then the floating static would be put into the routing table.
Moving to EIGRP adds value especially when there might be more than 1 way to get to the distance. While EIGRP and static routes might both be able to point to the best way to get there, there is advantage in EIGRP that if something happens and the primary path becomes invalid then EIGRP can dynamically recognize the issue and dynamically find an alternate path to put into the routing table and no manual intervention is required.
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