CiviCRM 4.7.8 error after upgrade on eWay Recurring
It looks like you had at some point set up the eWay Recurring extension.  Looked at the list of paths, it doesn't seem to be installed currently.

I looked at line 59 in Civi/Payment/System.php, which your error references.  It seems like that function is running based on the payment processors you have configured.

The solution is to either:
a) Install the eWay Recurring extension it's 4.7-compatible); or
b) Go to Administer menu » System Settings » Payment Processors and delete your payment processor that uses eWay Recurring.