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 Original Message (ID '108931') By jf: Solve is designed for polynomial equations. FindRoot can give numerical results as long as all parameters have numerical values. "e" was not given a constant value, or specified as a free parameter to solve for. Give it a constant value. (There are not enough equations to solve for seven variables.) In[6]:= With[{l = 0.344, m = 0.224, n = 0.134, e = 0.1}, FindRoot[{a*Cos[x] + b*Cos[y] == l, a*Cos[x + Pi/6] + b*Cos[z] == m, a*Cos[x + Pi/3] + b*Cos[k] == n, a*Sin[x] - e == b*Sin[y], a*Sin[x + Pi/6] - e == b*Sin[z], a*Sin[x + Pi/3] - e == b*Sin[k]}, {{x, 1}, {y, 1}, {z, 0.7}, {k, 0}, {a, 0.5}, {b, 0.5}}] ] Out[6]= {x -> 1.16296, y -> 0.378683, z -> 0.444204, k -> 0.281331, a -> 0.220185, b -> 0.27624}