Question

If the kinetic and potential energy in a system are equal, then the potential energy increases. What happens as a resul

Answer 1

-- If the system is 'closed', then nothing ... including energy ... can get in or out, and the total energy inside has to be constant.

If half of the energy in the system starts out as potential energy and the rest starts out as kinetic, and then the potential energy increases, there's only one place the increase could have come from ... it could only have been converted from kinetic energy.  So the kinetic energy in the system must decrease.

In fact, this isn't even a "result".  The kinetic energy has to decrease before the potential energy can increase, because that's where the increase has to come from.

If the system is 'open', then energy can come in and go out.  If the potential energy inside suddenly increases, we don't know where it came from, so we can't say anything about what happens to the system.