Sections with unidirectionally shared variables

Question

I have 2 sections is my notebook:

___________SECTION 1______________
Contains variables x y z
___________SECTION 2______________
Should copy over the values of x and y up to now, but make all changes to x
and y local to section 2

The idea is that if I set x = 2 in Section 1, then when the notebook is executed we will have x == 2 in Section 2. However, should I execute x = 3 in Section 2 and then go back and execute x in Section 1, it will still give me back x = 2 in section 1 because the changes to x are local to Section 2.

Meanwhile, if I do the same for z, which I did not make "local" to section 2, then the value for z will be altered in section 1 by what I do in section 2.

Thanks a lot for your help!

--- UPDATE ---

Okay, to make my problem clearer. I have a very long notebook in which I do many calculations with symbolic variables (matrices included). At some point, I arrive at the symbolic expression that I want and from that point onwards I want to begin substituting real values for the symbolic variables, e.g. what may have before been the symbolic variable AA I now substitute with {{a,b,c},{d,e,f},{g,h,i}}. My problem is that once I do this, execution of anything from the start of my document - which assumes symbolic variables - fails and throws lots of errors because now those symbolic variables are substituted with their definitions by Mathematica.

Since my notebook has 1000+ lines of code, I do not want to change anything in terms of how I write my expressions to avoid this "propagation from end to beginning of notebook" (too late for that, although for my future better coding your suggestions are welcome). Therefore, I am looking for a non-intrusive way to separate the section with symbolic variables and the section where these variables become substituted by their definitions. At the same time, I want the latter section to be able to use the previous (symbolic) section's results.

I hope this is a useful clarification. Thank you!

Answer 1

As @MarcoB states, you should probably use scoping constructs...

If you're opposed to that idea, you can set the Notebooks default context to be Unique to Each Cell Group. I wouldn't recommend that, but it works. You can set that under Evaluation > Notebook's Default Context > Unique to Each Cell Group:

Note, to escape this, you need to specify global variables like z in the correct context.

Answer 2

Note: shown below is an answer to the first version of the OP's question

---

Here is a simple example using scoping constructs, namely Block in this case. The idea is that you can indicate symbols to make local to Block, which implements dynamic scoping: take a look at the "Background and Context" section of its docs for a more complete explanation. Symbols not localized by Block will retain their global value and "accessibility", so they can be modified from within Block and the modification will be reflected outside of Block as well.

Clear[x, y, z]
x = 2; y = 4; z = 6;

Print["This is the Section 1 value of x: ", x]
Print["This is the Section 1 value of z: ", z]

Block[
  {x = x},
  Print["\nJust entered section 2; here is the current value of x: ", x];
  x = 3;
  Print["Now we changed the value of x local to Section 2; x == ", x];
  z = 8;
  Print["We also changed the value of z: z == ", z];
]

Print["\nNow we are back to Section 1:"]
Print["\tThe value of x is restored: x == ", x]
Print["\tThe value of z has changed: z == ", z]

And here is the output: