A high school booster club is selling raffle tickets for three different prizes. The tickets are $1 for the small prize, $2 for the medium prize, and $5 for the large prize. Shiloh spent $35 on 15 tickets. Together, the number of $2 and $5 tickets she bought is 1 more than the number of $1 tickets she bought. If x represents the number of $1 tickets, y represents the number of $2 tickets, and z represents the number of $5 tickets Shiloh bought, which system of equations represents this situation?