# Solving system of equations using NSolve?

Posted 2 months ago
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 Dear community I am a novice user of Mathematica. I am trying to find a solution to the following system of equation. Solution should be (Alpha = 0.7, Sigma = 0.7) Moreover, any hint about solving system of equation? V1[x1_, \[Sigma]_] = x1^\[Sigma] V2[y1_, \[Sigma]_] = y1^\[Sigma] F1[p1_] = Log[1/p1] F11[p1_, \[Alpha]_] = 1/Exp[(F1[p1])^\[Alpha]] V3[x2_, \[Sigma]_] = x2^\[Sigma] V4[y2_, \[Sigma]_] = y2^\[Sigma] F2[p2_] = Log[1/p2] F22[p2_, \[Alpha]_] = 1/Exp[(F2[p2])^\[Alpha]] NSolve[{V2[ 10, \[Sigma]] + (F11[ 0.3, \[Alpha]]*(V1[40, \[Sigma]] - V2[10, \[Sigma]])) == V3[5, \[Sigma]] + (F22[ 0.1, \[Alpha]]*(V3[150, \[Sigma]] - V4[5, \[Sigma]])), V2[30, \[Sigma]] + (F11[ 0.9, \[Alpha]]*(V1[40, \[Sigma]] - V2[30, \[Sigma]])) == V3[5, \[Sigma]] + (F22[ 0.7, \[Alpha]]*(V3[68, \[Sigma]] - V4[5, \[Sigma]]))}, {\[Alpha], \[Sigma]}] 
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Posted 2 months ago
 I would first get an idea of where a solution might be using a plot: eqs = {V2[ 10, \[Sigma]] + (F11[ 3/10, \[Alpha]]*(V1[40, \[Sigma]] - V2[10, \[Sigma]])) == V3[5, \[Sigma]] + (F22[ 1/10, \[Alpha]]*(V3[150, \[Sigma]] - V4[5, \[Sigma]])), V2[30, \[Sigma]] + (F11[ 9/10, \[Alpha]]*(V1[40, \[Sigma]] - V2[30, \[Sigma]])) == V3[5, \[Sigma]] + (F22[ 7/10, \[Alpha]]*(V3[68, \[Sigma]] - V4[5, \[Sigma]]))}; ContourPlot[Evaluate@eqs, {\[Alpha], -2, 2}, {\[Sigma], -2, 2}] and then approximate it with an iterative method: In[93]:= FindRoot[eqs, {{\[Alpha], 0.7}, {\[Sigma], 0.7}}] Out[93]= {\[Alpha] -> 0.713928, \[Sigma] -> 0.636601} 
 At the first attempt the plot range was random, but I was lucky. Then I collected the coordinates of the intersection with the mouse, using the "get coordinates" tool. IĀ used that value as seed for FindRoot.