prove that for any simple, connected graph G, if G has exactly one cycle, then G has the same number of nodes and edges

the hints are to use exercise 2 and theorem 7.

exercise 2 is a proof of "when an edge is removed from a cycle in a connected graph, the result is a graph that is still connected."

and theorem 7 is "if T is a tree with n edges, then T has n+1 vertices"

i'm completely lost, any ideas would be greatly appreciated

thanks!