Table of NSolve (and Solve) solutions creates extra unknown answers

Questions
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1

When I try to prepare a table of solution in the following way:

tt=Table[z/.NSolve[{x + y + z == 0, x - y == 0.5},{y, z}],{x, 0, 3, 0.1}]

I get the full answer for z: {{0.5),{0.3},{0.1},…,(-5.5}}

Applying tt//TableForm yields a column with:

0.5
0.3
0.1
etc.

The table can be transferred to Excell as a single column there and made use of there.

However, when the expressions (equations) are more complicated I get eight columns.
Columns 1-5 are unidentified (four of them complex numbers), No. 6 seems to be the answer z I am looking for and Nos. 7 and 8 contain zero only.

(In a simpler problem with only two variables x, y but quite complicated expression the number of columns is reduced to 5 with only one looking to be the correct answer y.)

Question: What do those 8 columns present and is one of them the correct answer z, indeed?

2

There are no special hidden meanings to the result of NSolve. But if you want help understanding the results you’re going to need to provide us with the actual example.

3

Thank you. Here it is:

k2 = 7.25941*10^-11
k1 = 3.7008*10^-10
kx = 3.15569*10^-8
kvv = 0.152304
vmax = 0.32
t6 = Table[p2 /. NSolve[{vt*n^2 == (4*(vmax - vt)^3*k2 + 2*n*(vmax - vt)^2*k1 + 
         n^2*(vmax - vt)*kx + p2*2*(vmax - vt)*kx^2*n^2/kvv)*p2, 
     n^3 == (8*(vmax - vt)^3*k2 + 2*n*(vmax - vt)^2*k1)*p2, 
     vt == 10^lvt}, {p2, n, vt}], {lvt, -4, -0.5, 0.05}]

Out[8]   {{-0.0038515 - 0.0304568 I, -0.0038515 + 0.0304568 I, 
  0.000199833}, {-0.00386354 - 0.0304558 I, -0.00386354 + 0.0304558 I,
   0.000224192}, {-0.00387704 - 0.0304546 I, -0.00387704 + 
   0.0304546 I, 
  0.000251516}, {-0.00389219 - 0.0304534 I, -0.00389219 + 0.0304534 I,
   0.000282167}, {-0.00390917 - 0.030452 I, -0.00390917 + 0.030452 I, 
  0.000316546}, {-0.00392823 - 0.0304504 I, -0.00392823 + 0.0304504 I,
   0.000355107}, {-0.0039496 - 0.0304488 I, -0.0039496 + 0.0304488 I, 
  0.000398354}, {-0.00397356 - 0.0304469 I, -0.00397356 + 0.0304469 I,
   0.000446855},  etc....

t6//TableForm

Out[9]  {{-3.49461*10^6, -2.44888*10^6 - 1.74943*10^6 I, -2.44888*10^6 + 
   1.74943*10^6 I, 594461. - 821951. I, 594461. + 821951. I, 0.419391,
   0., 0.}, {-3.49528*10^6, -2.44938*10^6 - 1.74884*10^6 I, -2.44938*10^6 + 1.74884*10^6 I, 
  595306. - 821454. I, 595306. + 821454. I, 0.592224, 0., 0.}, {-3.49604*10^6, -2.44995*10^6 - 
   1.74817*10^6 I, -2.44995*10^6 + 1.74817*10^6 I,  596254. - 820897. I, 596254. + 820897. I, 0.836248, 0., 
  0.}, {-3.49689*10^6, -2.45059*10^6 -  1.74742*10^6 I, -2.45059*10^6 + 1.74742*10^6 I, 
  597319. - 820274. I, 597319. + 820274. I, 1.18076, 0., 0.},  etc...
4

What do you mean by “unidentified”? You have a system of nonlinear polynomial equations, you can expect multiple solutions. In every row you get different solutions for a given value of lvt, I am not sure in what order. I supplied numerical values for vtn and p22:

k2 = 7.25941*10^-11; k1 = 3.7008*10^-10; kx = 
 3.15569*10^-8; kvv = 0.152304; vmax = 0.32; vtn = 1; p22 = 1; t6 = 
 Table[p2 /. 
   NSolve[{vtn^2 == (4 (vmax - vt)^3 k2 + 2 n (vmax - vt)^2 k1 + 
         n^2 (vmax - vt) kx + p22 (vmax - vt) kx^2 n^2/kvv) p2, 
     n^3 == (8 (vmax - vt)^3 k2 + 2 n (vmax - vt)^2 k1)*p2, 
     vt == 10^lvt}, {p2, n, vt}], {lvt, -4, -0.5, 0.05}]

Perhaps you are looking for real solutions only? If so, give NSolve the option Reals.

5

Thank you.
This answers my question.

6

If you accept only positive solution, you can add the condition to the equations:

t6 = Table[
  p2 /. NSolve[{vt*
       n^2 == (4*(vmax - vt)^3*k2 + 2*n*(vmax - vt)^2*k1 +
         n^2*(vmax - vt)*kx + p2*2*(vmax - vt)*kx^2*n^2/kvv)*p2,
     n^3 == (8*(vmax - vt)^3*k2 + 2*n*(vmax - vt)^2*k1)*p2,
     vt == 10^lvt,
     p2 > 0},
    {p2, n, vt}],
  {lvt, -4, -0.5, 0.05}]
7

Thank you

Indeed, I accept positive solutions only.