Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
Miranda went to play miniature golf on Monday, when it cost $16 to rent the club and ball, plus $1 per game. Debbie went Thursday, paying $6 per game, plus rental fees of $1. By coincidence, they played the same number of games for the same total cost. How many games did each one play? How much did each one spend?