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?

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).

Answer 1

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

Answer 2

2x+y=16 |*2
4x+2y=32
3x+2y=27
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4x-3x=32-27
x=5
2*5+y=16
10+y=16
y=16-10
y=6
The solution is (5,6)
The answer is the third, it is correct