How to solve this non-linear simultaneous equation?

syms C1 C2 C3 C4 C5 C6 C7
(((y116(1))/(C1 + C2 + C3 + C4 + C5 + C6 + C7))*X{3}) + (((y116(2))/C3 + C4 + C5 + C6)*X{4}) + ...
(((y116(3))/C2 + C5 + C6 + C7)*X{5}) + (((y116(4))/C4 + C7)*X{6}) + (((y116(5))/C6 + C7)*X{7}) + ...
(((y116(6))/C1 + C7)*X{8}) + (((y116(7))/C2 + C3 + C7)*X{9}) + (((y116(8))/C1 + C2 + C4 + C5 + C7)*X{10}) + ...
(((y116(9))/C2 + C3 + C4 + C6 + C7)*X{11}) + (((y116(10))/C1 + C4 + C5 + C6 + C7)*X{12}) + ...
(((y116(11))/C1 + C3 + C6 + C7)*X{13}) + (((y116(12))/C3 + C5 + C7)*X{14}) + (((y116(13))/C5 + C7)*X{15}) + ...
(((y116(14))/C1 + C2 + C7)*X{16}) == (X{3} + X{4} + X{5} + X{6} + X{7} + X{8} + X{9} + X{10} + X{11} +X{12} + X{13} + X{14} + X{15} + X{16})

I write this equation into MATLAB and run it. The result comes out as :

2*C2 + C3 + 2*C4 + 2*C5 + 2*C6 + 5*C7 + 165/(C1 + C2 + C3 + C4 + C5 + C6 + C7) + 586/C1 == 6
                                   2*C2 + 2*C3 + 2*C4 + 2*C5 + 2*C6 + 5*C7 + 165/(C1 + C2 + C3 + C4 + C5 + C6 + C7) + 288/C1 + 258/C2 == 6
                                  3*C3 + 2*C4 + 2*C5 + 3*C6 + 4*C7 + 165/(C1 + C2 + C3 + C4 + C5 + C6 + C7) + 104/C1 + 176/C2 + 90/C3 == 6
                        C2 + C3 + 4*C4 + 3*C5 + 3*C6 + 4*C7 + 165/(C1 + C2 + C3 + C4 + C5 + C6 + C7) + 255/C1 + 93/C2 + 50/C3 + 29/C4 == 6
                             C2 + 3*C4 + 5*C5 + 3*C6 + 5*C7 + 165/(C1 + C2 + C3 + C4 + C5 + C6 + C7) + 255/C1 + 82/C2 + 90/C3 + 29/C5 == 7
                          2*C3 + 3*C4 + 3*C5 + 5*C6 + 5*C7 + 165/(C1 + C2 + C3 + C4 + C5 + C6 + C7) + 209/C1 + 175/C2 + 50/C3 + 27/C6 == 7
 2*C2 + 3*C3 + 4*C4 + 5*C5 + 5*C6 + 12*C7 + 165/(C1 + C2 + C3 + C4 + C5 + C6 + C7) + 586/C1 + 258/C2 + 90/C3 + 29/C4 + 29/C5 + 27/C6 == 14 

How to solve this equation to find C1, C2, C3, C4, C5, C6, C7 ?

[darova]

did yoy try vpasolve?

[Alex Sha]

There are two solutions:

1:

c1: -6.86370996441933
c2: -16.2014399178883
c3: -27.492242477891
c4: -1.44190867129245
c5: -0.365190121706579
c6: -0.635231280035342
c7: 32.8706934181504

Feval:
2.8421709430404E-14
-7.28306304154103E-14
-9.85878045867139E-14
3.19744231092045E-14
2.8421709430404E-14
-4.9737991503207E-14
-3.5527136788005E-14

2:

c1: 6.39167498256291
c2: 12.4110032956383
c3: 25.8351415263511
c4: 1.40130483246744
c5: 0.373085024512327
c6: 0.690759107464528
c7: -30.2069654590374

Feval:
-2.55795384873636E-13
-2.16715534406831E-13
-2.1316282072803E-13
-1.88293824976427E-13
-2.98427949019242E-13
-2.34479102800833E-13
-5.6843418860808E-13