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I try to solve a system of equations, there are 4 eqs and 4 variables I need to get. There are some other symbolic constants as well. When I try to solve, it shows empty backets: Out[n]={}. Is it unsolvable or have I made a mistake?

dpds = w*(1 + d/n)*(1 - chi)*nsu*
   k*(1 + c)/chi/(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n))*(1 + 
     60*a*chi*(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n))^2/
         S/(1 - chi)/(1 + c)*(2*s + sigma)) + w*(1 + d/n)*k*nsu*b
dpdd = w*
   tau/n*(s/60*(1 - chi)*nsu*
      k*(1 + c)/(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n)) + 
     chi*a*(s + sigma)) + w/n*(s + sigma)*k*nsu*b
dpdy = -w*(1 + d/n)*(s + sigma)*k^2*nsu*
  rho*(1 - y/n)/(b - q - gamma*n)^2
dpdw = (1 + d/n)*s*(1 - chi)*nsu*
   k*(1 + c)/60/
     chi/(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n)) + (1 + 
    d/n) + (s + sigma)*a*nsu*
   k*(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n)) + 
  2*(1 + d/n)*(s + sigma)*k*nsu*b
dpdq = -w*(1 + d/n)*(s + sigma)*rho*(1 - y/n)*nsu*k*
  a/(b - q - gamma*n)^2
Solve[dpds == dpdd && dpds == dpdw && dpds == dpdy && 
  dpds == dpdq, {s, d, y, q}]
Anastasia
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    Welcome to MSE. The posted code is incomplete, e.g. dpds is not defined. Please fix it. – Rohit Namjoshi Mar 04 '20 at 16:04
  • What if any constraints exist on the variables and constants? Are any real, positive, negative, nonnegative, integer, ... Edit question with any additional info. – Bob Hanlon Mar 05 '20 at 03:58
  • @Rohit-Namjoshi You're right, thank you. I fixed it. – Anastasia Mar 05 '20 at 09:56
  • @Bob-Hanlon Well, all the constants and variables should be real and positive, but I'm not sure how it can help to make this code work. I just need symbolic expressions for 4 variables. – Anastasia Mar 05 '20 at 09:56

1 Answers1

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dpds = k*(1 + c)/
     chi/(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n))*(1 + 
     60*a*chi*(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n))^2/
         S/(1 - chi)/(1 + c)*(2*s + sigma)) + w*(1 + d/n)*k*nsu*b
dpdd = w*tau/
    n*(s/60*(1 - chi)*nsu*
      k*(1 + c)/(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n)) + 
     chi*a*(s + sigma)) + w/n*(s + sigma)*k*nsu*b
dpdy = -w*(1 + d/n)*(s + sigma)*k^2*nsu*
  rho*(1 - y/n)/(b - q - gamma*n)^2
dpdw = (1 + d/n)*s*(1 - chi)*nsu*
   k*(1 + c)/60/
     chi/(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n)) + (1 + 
    d/n) + (s + sigma)*a*nsu*
   k*(1 - rho*(b - q)/(b - q - gamma*n)*(1 - y/n)) + 
  2*(1 + d/n)*(s + sigma)*k*nsu*b
dpdq = -w*(1 + d/n)*(s + sigma)*rho*(1 - y/n)*nsu*k*
  a/(b - q - gamma*n)^2

I assume your first line is dpds..you should set your variables with = and not := have a look at this page for syntax infos 

Solve[dpds == dpdd && dpds == dpdw && dpds == dpdy && dpds == dpdq, {s, d, y, q}]

It's unclear if Solve can solve this even, I gave up after 10 minutes....

DrMrstheMonarch
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