One group of people purchased 10 hot dogs and 5 soft drinks for $35. another group purchased 7 hot dogs and 4 soft drinks for $25.25. what is the cost of a single hot dog? a single soft drink?

10 H + 5 D = $35         times all by 4      40 H + 20 D =  $140.00
  7 H + 4 D = $25.25  times all by  5    -  35 H - 20 D    = -126.25 and subtract
 Subtract                                                  5 H          =  $13.75
 Divide by 5 to find price of one hot dog          H          =  $2.75

10 ($2.75) + 5 D = $35  input cost of one hot dog into first equation
   $27.50  + 5 D  =   $35.00
- $27.50              = -$27.50
                   5 D  = $ 7.50 divide by 5 so one drink is $1.50 then go back and check