System of algebraic equations with 6 variables

Questions
,
1

Hello,

I am new to Mathematica, and I just downloaded it tonight. I need to do a very specific procedure: calculate a complicated system of equations in 6 variables. I have tried for hours on end to do this, following the instructions as they are listed in Mathematica: “In a system of equations with multiple variables, you can solve for some or all of the variables by using a list in the second argument.” I have done so, but my answer is given as one number, which makes no sense. My work is given below.

    Solve[{44826600000*a+406601000000*b+
    134691918588*c+656526*f+512206908*e+170700546*d-7642032.5==0,3757520000000*b
    +406601000000*a+1233170000000*c+5925820*f+4678814294*e+
    1544327542*d-69097900==0, 406601000000*c+134692000000*a+
    1233170000000*b+1967580*f+1544327592*e+512206908*d -22936700==0,
 170700546*a+1544327592*b+512206908*c+2550*f+1967580*e+656526*d-29327.5==0, 
512206908*a+4678814150*b+1544327592*c+7634*f+5925818*e+1967580*d-87833==0, 
10*f+656526*a+5925820*b+1967580*c+7634*e+2550*d-113.5==0},
    {a,b,c,d,e,f}]
    
    Answer: 4.06601 x 10^11.

What is this answer??? I should be getting a different value for a, b, c, d, e, and f, not a single number. Can someone please help me and tell me what exactly I am doing wrong?

Thanks!

2

eq = Rationalize[{44826600000 a + 406601000000 b + 134691918588 c +
656526 f + 512206908 e + 170700546 d - 7642032.5 == 0,
3757520000000 b + 406601000000 a + 1233170000000 c + 5925820 f +
4678814294 e + 1544327542 d - 69097900 == 0,
406601000000 c + 134692000000 a + 1233170000000 b + 1967580 f +
1544327592 e + 512206908 d - 22936700 == 0,
170700546 a + 1544327592 b + 512206908 c + 2550 f + 1967580 e +
656526 d - 29327.5 == 0,
512206908 a + 4678814150 b + 1544327592 c + 7634 f + 5925818 e +
1967580 d - 87833 == 0,
10 f + 656526 a + 5925820 b + 1967580 c + 7634 e + 2550 d -
113.5 == 0}, 0];(Solve command likes exact numbers)

sol = Solve[eq, {a, b, c, d, e, f}]

(* {{a -> 37661875233681469616020337/19800425780012197006195422, 
  b -> 4550701523122289471303/3300070963335366167699237, 
  c -> -(32764554758922235536810499/79201703120048788024781688), 
  d -> -(6432963255964509656326286590/9900212890006098503097711), 
  e -> 333715554775186346083975250/3300070963335366167699237, 
  f -> 145896220294933276857947910233/3300070963335366167699237}}*)

sol // N

(*{{a -> 1.90207, b -> 0.00137897, c -> -0.413685, d -> -649.78, 
  e -> 101.124, f -> 44210.}}*)
3

That worked perfectly. Thank you so much!

4

I cannot replicate this behavior.

In[398]:= Solve[{44826600000*a + 406601000000*b + 134691918588*c + 
    656526*f + 512206908*e + 170700546*d - 7642032.5 == 0, 
  3757520000000*b + 406601000000*a + 1233170000000*c + 5925820*f + 
    4678814294*e + 1544327542*d - 69097900 == 0, 
  406601000000*c + 134692000000*a + 1233170000000*b + 1967580*f + 
    1544327592*e + 512206908*d - 22936700 == 0, 
  170700546*a + 1544327592*b + 512206908*c + 2550*f + 1967580*e + 
    656526*d - 29327.5 == 0, 
  512206908*a + 4678814150*b + 1544327592*c + 7634*f + 5925818*e + 
    1967580*d - 87833 == 0, 
  10*f + 656526*a + 5925820*b + 1967580*c + 7634*e + 2550*d - 113.5 ==
    0}, {a, b, c, d, e, f}]

During evaluation of In[398]:= RowReduce::luc: Result for RowReduce of badly conditioned matrix {{656526.,5.12206908*10^8,1.70700546*10^8,1.34691918588*10^11,4.06601*10^11,4.48266*10^10,-7.6420325*10^6},{5.92582*10^6,4.678814294*10^9,1.544327542*10^9,1.23317*10^12,3.75752*10^12,4.06601*10^11,-6.90979*10^7},{<<1>>},<<1>>,{7634.,5.925818*10^6,<<4>>,-87833.},{10.,7634.,2550.,1.96758*10^6,5.92582*10^6,656526.,-113.5}} may contain significant numerical errors.

Out[398]= {{a -> 1.90207400851, b -> 0.00137897080916, 
  c -> -0.413684977324, d -> -649.780295374, e -> 101.12375112, 
  f -> 44210.0251526}}