Answer:
Corresponding system of equations is,
and 
Step-by-step explanation:
Let, the number of hot dogs = x and the number of hamburgers = y
It is given that, the concession sold total 230 hot dogs and hamburgers.
Thus, we have,
.
Also, the price of each hot dog and hamburger are $0.50 and $0.75 each.
Since, the total earnings is $138.50.
We get, 
Thus, the corresponding system of equations is,

