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Python 3.6, 96 93 (95-2) bytes

a,b=0,1
f=open(__file__,"r+");next(f);f.write(f"a,b={b,a+b}\n{next(f)}{f.‌​seek(0)}");print(b)

hardcoding the filename would save 5 bytes (90 bytes):

a,b=0,1
f=open("f","r+");next(f);f.write(f"a,b={b,a+b}\n{next(f)}{f.‌​seek(0)}");print(b)

Saved some bytes thanks to @Artyer

Python 3.6, 96 91 (93-2) bytes

a,b=0,1
f=open(__file__,"r+");next(f);f.write(f"a,b={b,a+b}\n{next(f)}{f.seek(0)}");print(b)

hardcoding the filename would save 5 bytes (88 bytes):

a,b=0,1
f=open("f","r+");next(f);f.write(f"a,b={b,a+b}\n{next(f)}{f.seek(0)}");print(b)

Saved some bytes thanks to @Artyer

Python 3.6, 96 94 (96-2) bytes

a,b=0,1
f=open(__file__,"r+");s=f.readlines()[1];f.seek(0);f.write(f"a,b={b,a+b}\n"+s);print(b)

hardcoding the filename would save 5 bytes (91 bytes):

a,b=0,1
f=open("f","r+");s=f.readlines()[1];f.seek(0);f.write(f"a,b={b,a+b}\n"+s);print(b)

Python 3.6, 96 93 (95-2) bytes

a,b=0,1
f=open(__file__,"r+");next(f);f.write(f"a,b={b,a+b}\n{next(f)}{f.‌​seek(0)}");print(b)

hardcoding the filename would save 5 bytes (90 bytes):

a,b=0,1
f=open("f","r+");next(f);f.write(f"a,b={b,a+b}\n{next(f)}{f.‌​seek(0)}");print(b)

Saved some bytes thanks to @Artyer

Python 3.6, 96 94 (96-2) bytes

a,b=0,1
f=open(__file__,"r+");s=f.readlines()[1];f.seek(0);f.write(f"a,b={b,a+b}\n"+s);print(b)

Python 3.6, 96 94 (96-2) bytes

a,b=0,1
f=open(__file__,"r+");s=f.readlines()[1];f.seek(0);f.write(f"a,b={b,a+b}\n"+s);print(b)

hardcoding the filename would save 5 bytes (91 bytes):

a,b=0,1
f=open("f","r+");s=f.readlines()[1];f.seek(0);f.write(f"a,b={b,a+b}\n"+s);print(b)