Maya had $27. She spent all the money on buying 3 burgers for $x each and 2 sandwiches for $y each. If Maya had bought 2 burgers and 1 sandwich, she would have been left with $11.

A student concluded that the price of each burger is $5 and the price of each sandwich is $6. Which statement best justifies whether the student's conclusion is correct or incorrect?

The student's conclusion is correct because the solution to the system of equations 3x + 2y = 11 and 2x + y = 16 is (5, 6).
The student's conclusion is incorrect because the solution to the system of equations 3x − 2y = 11 and 2x − y = 16 is (5, 6).
The student's conclusion is correct because the solution to the system of equations 3x + 2y = 27 and 2x + y = 16 is (5, 6).
The student's conclusion is incorrect because the solution to the system of equations 2x + 3y = 27 and x + 2y = 16 is (5, 6).