Let x be the cost of each turkey sandwich and y be the cost of each roast beef sandwich.
From the first platter, which costs $33 and contains 2 turkey sandwiches and 3 roast beef sandwiches, we can write the equation:
2x + 3y = 33
From the second platter, which costs $32 and contains 3 turkey sandwiches and 2 roast beef sandwiches, we can write the equation:
3x + 2y = 32
Now we have a system of two linear equations in two variables:
2x + 3y = 33
3x + 2y = 32
To solve for x and y, we can use the method of elimination. Multiplying the first equation by 2 and the second equation by -3, we get:
4x + 6y = 66
-9x - 6y = -96
Adding these equations, we get:
-5x = -30
Dividing both sides by -5, we get:
x = 6
Now we can substitute x = 6 into either of the original equations to solve for y. Using the first equation, we get:
2(6) + 3y = 33
12 + 3y = 33
3y = 21
y = 7
Therefore, each turkey sandwich costs $6 and each roast beef sandwich costs $7.