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How to solve the system of linear equations?

Dear Mathematica experts,

How to solve, in Mathematica, the system of linear equations,

when a number of equations is larger than a number of variables.

Another system easily pass to apply LSM in this case, but it seems to
me that there is no such opportunity in Mathematica.

As an application, given N>5 points at plane, how to calculate (the
parameters) of best fitting ellipse. 

Thanks a lot,

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