At a concession stand, seven hot dogs and two hamburgers cost $11.00, two hot dogs and seven hamburgers cost $16.00. Find the cost of one hot dog and the cost of one hamburger.

Answer 1

7d+2b = 11
2d+7b = 16

5d + 2(d+b) = 11
5b + 2(d+b) = 16
add the equations and you get
5(d+b) + 4(d+b) = 27
9(d+b) = 27
d+b = 3

similarly, b-d = 1

b=2
d=1

dog costs $1
burger costs $2