Elements of a complex system of the linear equations 

You introduced the following system of the equations 
Solution of a system following 
Sets of the linear equations quite often meet in daily calculations therefore methods of their decision great variety is thought up. But before consideration of the simplest algorithm of finding of unknown it is worth remembering what in general the system of such equations can have:
 to have only one right decision;
 to have an infinite set of roots;
 to have not joint type (when decisions cannot be).
Gauss's method used by ours of ABACUSES boat  the most powerful and troublefree tool for search of the solution of any system of the equations of linear type.
Returning to terms of the higher mathematics, Gauss's method can be formulated so: by means of elementary transformations the system of the equations has to be brought to the equivalent system of triangular type (or socalled step type) from which gradually, since the latest equation, there are remained variables. At all this elementary transformations over systems  exactly the same, as elementary transformations of matrixes in transposition for lines.
Our boat is able to issue immediately solutions of a system of the linear equations with unlimited number of variables!
Practical application finds the solution of such systems in electrical equipment and geometry: calculations of currents in difficult contours and removal of the equation of a straight line when crossing three planes and also in a set of specialized tasks.
This service allows to solve the system of the linear equations, unlimited by the sizes, with complex coefficients.
You introduced the following system of the equations 
Solution of a system following 
Also we receive the following result.