Question

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?

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

Answer 1

Let
x-------> the cost of the burger
y-------> the cost of the sandwiches

we know that
3x+2y=27-----> equation 1
2x+y=27-11-----> 2x+y=16-----> multiply by -2-----> -4x-2y=-32--> equation 2

adds equation 1 and equation 2
 3x+2y=27
-4x-2y=-32
----------------
-x=27-32-----> x=5
3*5+2y=27----> 2y=27-15-----> y=6

therefore

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