IMO 1976 LL CZS9

Find all (real) solutions of the system

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IMO 1976 LL CZS9

Origin: CZS

Problem

Find all (real) solutions of the system 3x1 −x2 −x3 −x5 = 0, −x1 + 3x2 −x4 −x6 = 0, −x1

  • 3x3 −x4 −x7 = 0, −x2 −x3 + 3x4 −x8 = 0, −x1
  • 3x5 −x6 −x7 = 0, −x2 −x5 + 3x6 −x8 = 0, −x3 −x5
  • 3x7 −x8 = 0, −x4 −x6 −x7 + 3x8 = 0.