You don't need 10 lb line to catch 10 lb carp - you can use your trout rod and really have some fun with those fish. Use sharp hooks. Bread, corn, or dough baits are where it's at. Double chk the regs though, to make sure you can use bait in that stream.
My favorite carp rigs for average (5-10lb fish) are a long light spinning rod (or a fly rod with spin reel mounted) and 4 or 6lb test line. I use a single #6 or #4 octopus style hook (gamakatsu or owner) and either leave it at that, or I peg a large corkie 1 and 1/2 times the water depth above it with a tooth pick to use as a strike indicator. I usually use bread for carp bait, whole wheat or multigrain if it's cheap. I tear off chunks, and press the bread around the hook into a firm ball or pyramid shape - this provides enough casting weight for a 25-30 foot cast. If you use the strike indicator - look for it to bobble then just start swimming off.
My best carp was a 20lber on 4lb line. That was a strain on the tackle for sure - took me about half an hour to land it. Your average 5-10lb fish can be brought to hand in 10 minutes or less.