Steve went to the concession stand and bought hamburgers and hot dogs for the kids he brought to watch a baseball game. Each child chose either one hamburger or one hotdog. Hot dogs cost $1.50 each and hamburgers cost $2.75 each. Steve spent a total of $23.75 on 10 kids. (a) Could Steve have bought an equal amount of hamburgers and hot dogs? Justify your answer.
(b) If x represents the number of hotdogs purchased and y represents the number of hamburgers purchased, write a system of equations that models this situation and determine the number of both items bought.