Vtyjkyuk

Does anybody know how to save the intermediate results inside a while function in a table?
Here is my code. I would like to save the x,y,counter values in a table in every step that while takes. Thank you!

counter = 0;
While[counter < 5,
 counter = counter + 1;
 sol = NSolve[2 x + y - counter == 0, 
 3 y + 5 x - 2 counter == 0, x, y];
 ]

counter = 0;
sol = ;
While[counter < 5, counter = counter + 1;
 AppendTo[sol, Flatten[counter, x, y /. 
 NSolve[2 x + y - counter == 0, 3 y + 5 x - 2 counter == 0, x, y]]]]

sol

1, 1., -1., 2, 2., -2., 3, 3., -3., 4, 4., -4., 5, 5., -5.

or

counter = 0;
sol2 = ConstantArray[0, 5];
While[counter < 5, counter = counter + 1;
 sol2[[counter]] = Flatten@counter, x, y /. 
 NSolve[2 x + y - counter == 0, 3 y + 5 x - 2 counter == 0, x, y]]
sol2

1, 1., -1., 2, 2., -2., 3, 3., -3., 4, 4., -4., 5, 5., -5.

Use Sow and Reap :

counter = 0;
Reap @ While[counter < 5, counter = counter + 1;
 sol = NSolve[2 x + y - counter == 0, 
 3 y + 5 x - 2 counter == 0, x, y];
 Sow[x, y, counter /. sol]]

I think other answer take your question too literally. You do not really need While. IMHO Mathematica way of solving this is to use Table.

Assuming, that your equation always gives a single solution:

Table[
 x, y, counter /. 
 First@NSolve[2 x + y - counter == 0, 
 3 y + 5 x - 2 counter == 0, x, y], counter, 5] // TableForm

To reach the same end, as you mentioned Table (a digression: if you know Python, you can compare Wolfram's Table with its list comprehensions, which is attached with more conciseness and readability.), the most direct method is just to use it:

Table[
 Append[
 NSolve[2 x + y - counter == 0, 3 y + 5 x - 2 counter == 0, x, y],
 counter
 ], 
 counter, 4
 ]

x -> 1., y -> -1., 1, x -> 2., y -> -2., 2,
x -> 3., y -> -3., 3, x -> 4., y -> -4., 4