Lets use these variables for each bag:
Bag 1 = a
Bag 2 = b
Bag 3 = c
Bag 4 = d
Bag 5 = e
Bag 6 = f
Bag 7 = g
Now set up the following system of equations
a + b = 57
b + c = 83
c + d = 71
d + e = 43
e + f = 66
f + g = 43
Also since we know how many marbles there are total, we can use this equation:
a+b+c+d+e+f+g=200
Now subtract (a+b=57), (c+d=71), and (f+g=43) from a+b+c+d+e+f+g=200 to eliminate everything but one bag (in this case bag 5 which is denoted "e")
a+b+c+d+e+f+g=200
-(a+b =57)
-( c+d =71)
-( f+g=43)
-------------------
e =29
So we know that bag 5 has 29 marbles
Now plug in e=29 to find f
Bag 6:
29 + f = 66
f = 37
So we know that bag 6 has 37 marbles
Now plug in f=37 to find g
Bag 7:
37 + g = 43
g = 6
So we know that bag 7 has 6 marbles
Now plug in e=29 to find d
Bag 4:
d + 29 = 43
d = 14
So we know that bag 4 has 14 marbles
Now plug in d=14 to find c
Bag 3:
c + 14 = 71
c = 57
So we know that bag 3 has 57 marbles
Now plug in c=57 to find b
Bag 2:
b + 57 = 83
b = 26
So we know that bag 2 has 26 marbles
Now plug in b=26 to find a
Bag 1:
a + 26 = 57
a = 31
So we know that bag 1 has 26 marbles
So here's a summary of all of the bags:
Bag 1 = 31 marbles
Bag 2 = 26 marbles
Bag 3 = 57 marbles
Bag 4 = 14 marbles
Bag 5 = 29 marbles
Bag 6 = 37 marbles
Bag 7 = 6 marbles
Check:
31+26+57+14+29+37+6=200
200=200