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based on an earlier version of the Wolfram Language.
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Solve[eqns, vars]
attempts to solve an equation or set of equations for the variables vars.
Solve[eqns, vars, elims]
attempts to solve the equations for vars, eliminating the variables elims.
  • Equations are given in the form lhsrhs.
  • Simultaneous equations can be combined either in a list or with &&.
  • A single variable or a list of variables can be specified.
  • Solve[eqns] tries to solve for all variables in eqns.
  • Solve gives solutions in terms of rules of the form x->sol.
  • When there are several variables, the solution is given in terms of lists of rules: {x->sx, y->sy, ...}.
  • When there are several solutions, Solve gives a list of them.
  • When a particular root has multiplicity greater than one, Solve gives several copies of the corresponding solution.  »
  • Solve deals primarily with linear and polynomial equations.
  • Solve gives generic solutions only. It discards solutions that are valid only when the parameters satisfy special conditions. Reduce gives the complete set of solutions.  »
  • Solve will not always be able to get explicit solutions to equations. It will give the explicit solutions it can, then give a symbolic representation of the remaining solutions in terms of Root objects. If there are sufficiently few symbolic parameters, you can then use N to get numerical approximations to the solutions.  »
  • Solve gives {} if there are no possible solutions to the equations.  »
  • Solve gives {{}} if all variables can have all possible values.  »
  • Solve[eqns, ..., Mode->Modular] solves equations with equality required only modulo an integer. You can specify a particular modulus to use by including the equation Modulusp. If you do not include such an equation, Solve will attempt to solve for the possible moduli.  »
  • Solve uses special efficient techniques for handling sparse systems of linear equations with approximate numerical coefficients.
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