Solve
 Usage
• 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.
Notes
• Equations are given in the form lhs  rhs. • 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. • Example: Solve[3 x + 9 0, x]. • 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 ->  , y ->  , ... }. • 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. • The option InverseFunctions specifies whether Solve should use inverse functions to try and find solutions to more general equations. The default is InverseFunctions->Automatic. In this case, Solve can use inverse functions, but prints a warning message. See notes on InverseFunctions. • 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. • See also: Reduce, FindInstance, Eliminate, SolveAlways, Roots, NSolve, FindRoot, LinearSolve, RowReduce, GroebnerBasis, DSolve, Root, RSolve. • New in Version 1; modified in 3.
| 
