4PM1/01R Jun 2020, Question 9: Exponential Equations
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks
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The question, in short
Use algebra to solve the simultaneous equations 16^x ÷ 8^y = 1/4 and 4^x × 2^y = 16, showing working clearly.
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Solution · 7 marks
- 116^x/8^y = 1/4 ⇒ 2^(4x)/2^(3y) = 2^(−2) ⇒ 4x − 3y = −2
- 24^x 2^y = 16 ⇒ 2^(2x + y) = 2⁴ ⇒ 2x + y = 4
- 3Double the second: 4x + 2y = 8
- 4Subtract: 5y = 10 ⇒ y = 2
- 52x + 2 = 4 ⇒ x = 1
Answerx = 1, y = 2
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