ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

212 BRAHMAGUPTA AS AN ALGEBRAIST
The total value (of the unknown quantities) plus or
minus the individual values (of the unknowns) multi-
plied by an optional number deing severally (given),
the sum (of the given quantities) divided by the num-
ber of unknowns increased or decreased by the multi-
plier will be the total value; thence the rest (can be
determined).¹
Σx±cx₁=a₁, Σx±cx₂=a₂, Σx±cx₃=a₃,......
Σx±cx =an
Therefore
Σx = (a₁ + a₂ + a₃ + ...... + an) / (n ± c)
Hence
x₁ = 1/c ( ±a₁ ∓ (a₁ + a₂ + a₃ + ...... + an) / (n ± c) );
and so on for x₂, x₃ etc.
Now we shall give the rule enunciated by Brahmagupta
for solving linear equations involving several unknowns :
Removing the other unknowns from (the side of) the