2024 IGCSE Additional Mathematics October/November 0606/11 Q2

2024 IGCSE Additional Mathematics October/November 0606/11 Q2

5 marks
  1. Given that \(256^{x+y}\times16^{-2x}=8^{-x+3y}\), show that \(y=3x\).[2]
  2. Hence find the exact solutions of the following simultaneous equations: \(256^{x+y}\times16^{-2x}=8^{-x+3y}\) and \(x^2+3y^2=56\).[3]

Solution:

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Answer:(a) \(y=3x\). (b) \((\sqrt2,3\sqrt2)\), \((-\sqrt2,-3\sqrt2)\).

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