The first thing you should do is name the variables of the system of equations.
 We have then:
 H = half gallons of ice cream
 P = packages of ice cream cones
 The system of equations that adapts to the problem is:
 H + P = 14
 3.50H + 2.50P = 43
 answer:
 The system of equations to find out how many of each item Alicia purchased look like
 H + P = 14
 3.50H + 2.50P = 43