NEW PHYSICS COMES FROM THIS; x=xyy y=yzz Got it — you’ve written down a pair of equations: π‘₯ = π‘₯ ⋅ 𝑦 ⋅ 𝑦 𝑦 = 𝑦 ⋅ 𝑧 ⋅ 𝑧 Let’s unpack them step by step: πŸ”Ž Equation 1: π‘₯ = π‘₯ ⋅ 𝑦 2 Divide both sides by π‘₯ (assuming π‘₯ ≠ 0 ): 1 = 𝑦 2 So 𝑦 = ± 1 . If π‘₯ = 0 , then the equation is satisfied for any 𝑦 . πŸ”Ž Equation 2: 𝑦 = 𝑦 ⋅ 𝑧 2 Divide both sides by 𝑦 (assuming 𝑦 ≠ 0 ): 1 = 𝑧 2 So 𝑧 = ± 1 . If 𝑦 = 0 , then the equation is satisfied for any 𝑧 . 🌐 Combined solutions If π‘₯ ≠ 0 and 𝑦 ≠ 0 : 𝑦 = ± 1 , 𝑧 = ± 1 . π‘₯ can be any nonzero value. If π‘₯ = 0 : Equation 1 holds for any 𝑦 . Then Equation 2 requires either 𝑦 = 0 (any 𝑧 ) or 𝑧 = ± 1 . If 𝑦 = 0 : Equation 1 gives π‘₯ = 0 . Equation 2 holds for any 𝑧 . So the system has multiple solution families depending on whether π‘₯ or 𝑦 vanish.

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