In equation, let x be the number of male students
a be the number of adults
y be the number of female students.
x= 7a+1
a= x/7 -1
y= x/2 or (7a + 1)/ 2
a + b = 82, let b be the number of students.
a + (x + y) = 82
a + [7a+1 + (7a+1)/2] = 82
a + [{2(7a+1) + 7a+1} / 2] = 82
a + [(14a +2 + 7a +1) / 2] = 82
a + [(21a + 3) / 2] = 82
(2a+ 21a + 3) / 2 = 82
(23a + 3) / 2 = 82
23a + 3 = 164
23a = 164 -3
23a = 161
a = 7
x = 7(7) +1, 49+1 = 50 male students
y=x/2, 50/2, 25 female students
50(male students) + 25(female students) + 7 (adults) = 82
The answer is -7.20 click on file for more details.
Answer:
The solution for this system is: 
Step-by-step explanation:
The problem states that we have to solve this system by the elimination method
In the elimination method, we transform the system in such a way that one variable can cancel each other. With this, we find the result of the other variable. Then, we can replace the variable we found in any of the equations, and we have the value of the variable that we had initially canceled.
In this problem, we have the following system:


If we add equations 1) and 2), the variable x is going to be eliminated





Now, we can replace the value of y in any of the equations, to find x:
I will replace in equation 2)





The solution for this system is: 