Theo bought 4 hot dogs and 3 sodas for $6.55. at the same concession stand, vicky bought 2 hot dogs and 5 sodas for $4.85. what is the price of a hot dog?

Let the price of a hot dog be h and price os a soda be s dollars. Then we have:-

4h + 3s = 6.55(1)
2h + 5s = 4.85    multiply this equation by -2:-
-4h -10s = -9.70(2)

Adding (1) and (2):-

-7s =  -3.15
s = -3.15 / -7 =  0.45

So $0.45 is the price of a soda
To find price of a hot doe plug s = 0.45 into equation (1):-

4h = 3(0.45) = 6.55
4h =  6.55-1.35 = 5.20

h = 5.20 / 4 =  $1.30

The answer is  price hot dog = $1.30