A Set of Simultaneous Equations

On page 94 of the Journal Mr. S. Ramanujan has discussed the solution by ' partial fractions,' of the following set of equations :-

X₁+X₂+X₃+ ..... .... X_n =a₁

X₁Y₁+X₂Y₂+X₃Y₃+ ..... .... X_nY_n...... =a₂