Example 10 (2001 National High School Competition Question) It is known that the sum of the prices of 6 roses and 3 carnations is greater than 24 yuan, and the sum of the prices of 4 roses and 5 carnations is less than 22 yuan. Then the comparison result of the price of 2 roses and the price of 3 carnations is ( ).
A. The price of 2 roses is higher
B. The price of 3 carnations is higher
C. The prices are the same
D. Uncertain
Solution: Choose A. Reason: Let the unit prices of roses and carnations be $x$ and $y$ yuan per stem, respectively, then $6x + 3y > 24, 4x + 5y \leq 24, 4x + 5y = \frac{1}{9}(11 \times 24 - 12 \times 22) = 0$,
which means $2x > 3y$.
Note: The region represented by a system of linear inequalities can also be used to study this.