Answer :
Answer:
Option C
The student's conclusion is correct because the solution to the system of equations [tex]3x+2y=27[/tex] and [tex]2x+y=16[/tex] is [tex](5,6)[/tex]
Step-by-step explanation:
Let
x------> the cost of each burger
y-----> the cost of each sandwich
we know that
[tex]3x+2y=27[/tex] -----> equation A
[tex]2x+y=(27-11)[/tex]
[tex]2x+y=16[/tex] ----> equation B
Solve the system of equations
Multiply the equation B by [tex]-2[/tex]
[tex]-2(2x+y)=-2*16[/tex] ----->[tex]-4x-2y=-32[/tex] ------> equation C
Adds equation A and equation C
[tex]3x+2y=27 \\-4x-2y=-32\\ ----------\\ 3x-4x=27-32\\ -x=-5\\x=5[/tex]
Substitute the value of x in the equation B
[tex]2(5)+y=16[/tex]
[tex]10+y=16[/tex]
[tex]y=6[/tex]
The solution of the system of equations is the point [tex](5,6)[/tex]
so
The price of each burger is [tex]\$5[/tex]
The price of each sandwich is [tex]\$6[/tex]