A café sells two types of sandwiches, vegetable and cheese. Three vegetable sandwiches and two cheese sandwiches together cost Rs 118, while two vegetable sandwiches and one cheese sandwich together cost Rs 78.
(i) Represent the above information as a system of linear equations in the variables x (price of a vegetable sandwich) and y (price of a cheese sandwich).
(ii) Write down the coefficient matrix A and the constant matrix B for the system.
(iii) Find A−1 and hence determine the prices of the two sandwiches.