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 Original Message (ID '551489') By Bill Simpson: In Response To 'Re: Re: Solve nonlinear algberic euations' --------- I did not get the "cannot solve with methods" error that you did. Perhaps my version is different. Can you use this to solve for three of your variables and then substitute the results into a smaller problem to solve for the rest? In[1]:= \[Rho]0 = 127/100; p0 = 1013*10^2; p1 = 3*p0; \[Gamma] = 14/10; \[Phi]1 = 30*(Pi/180); Simplify[Reduce[{ \[Rho]0*u0*Sin[\[Phi]1] == \[Rho]1*u1*Sin[\[Phi]1 - \[Theta]1], \[Rho]1*u1*Sin[\[Phi]2] == \[Rho]2*u2*Sin[\[Phi]2 - \[Theta]1], p0 + \[Rho]0*(u0*Sin[\[Phi]1])^2 == p1 + \[Rho]1*(u1*Sin[\[Phi]1 - \[Theta]1])^2, p1 + \[Rho]1*(u1*Sin[\[Phi]2])^2 == p2 + \[Rho]2*(u2*Sin[\[Phi]2 - \[Theta]1])^2, \[Gamma]*(p0/((\[Gamma] - 1)*\[Rho]0)) + (1/2)*(u0*Sin[\[Phi]1])^2 == \[Gamma]*(p1/((\[Gamma] - 1)*\[Rho]1)) + (1/2)*(u1*Sin[\[Phi]1 - \[Theta]1])^2, \[Gamma]*(p1/((\[Gamma] - 1)*\[Rho]1)) + (1/2)*(u1*Sin[\[Phi]2])^2 == \[Gamma]*(p2/((\[Gamma] - 1)*\[Rho]2)) + (1/2)*(u2*Sin[\[Phi]2 - \[Theta]1])^2 }, {u0, u1, u2}]] Out[6]= ...LargeResultSnipped... The result is large and complicated, but there are some repeated items and you might be able to use information you have about your angles being Real and other information to obtain small values for your variables. If you have any additional information about the domain of any of your variables then this might help, but sometimes that information will make Reduce slower.