Do bears kill elk and then do the coyotes eat remains?

It's possible, but not a common scenario. Here's why:

* Bears are capable of killing elk: Large bears, especially grizzly bears, are powerful enough to take down elk. However, bears usually prefer easier meals like berries, fish, and carrion.

* Coyotes are opportunistic scavengers: Coyotes are known to scavenge on carcasses left by larger predators. They would likely take advantage of an elk killed by a bear, but they aren't the primary predator in this situation.

* Competition and hierarchy: Bears are higher on the food chain than coyotes. If a bear has killed an elk, it's likely to defend its kill from coyotes, especially if it's hungry.

More likely scenarios:

* Bears kill elk and eat them: This is the most common outcome. Bears have the strength and hunting skills to kill and consume elk.

* Wolves kill elk and coyotes scavenge: Wolves are more efficient elk hunters than bears and coyotes. Coyotes often follow wolf packs to scavenge on the leftovers.

* Elk die naturally and coyotes scavenge: Elk can die from various causes like disease, accidents, or old age. Coyotes readily scavenge on these carcasses.

So, while a bear killing an elk and a coyote scavenging on the remains is possible, it's not the most likely scenario. The exact interactions between these animals depend on factors like the specific location, time of year, and availability of other food sources.