Answer: the cost of a cheeseburger is $4
Explanation:
Let x represent the cost of one cheeseburgers.
Let y represent the cost of one Soda.
The patriot diner sells 2 cheeseburgers and one soda for $11.00. It means that
2x + y = 11 - - - - - - - - - - - 1
She also sells 3 cheeseburgers and 2 sodas for $18.00. It means that
3x + 2y = 18 - - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by 2, it becomes
6x + 3y = 33
6x + 4y = 36
Subtracting, it becomes.
- y = - 3
y = 3
Substituting y = 3 into equation 1, it becomes
2x + 3 = 11
2x = 11 - 3 = 8
x = 8/2 = 4