The number of solutions of 3 x + y = 243 and 243 x − y = 3 is

(a) 0  (b) 1   (c) 2   (d) infinite

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Question 40 The number of solutions of 3x + y = 243 and 243x − y = 3 is (a) 0 (b) 1 (c) 2 (d) infinite 3x + y = 243 3x + y = 35 Comparing powers x + y = 5 243x − y = 3 (35)x − y = 3 35(x − y) = 31 Comparing powers 5(x − y) = 1 x − y = 𝟏/𝟓 Adding (1) and (2) (x + y) + (x − y) = 5 + 1/5 2x = (5(5) + 1)/5 2x = (25 + 1)/5 2x = 26/5 x = 𝟏𝟑/𝟓 Putting value of x in (1) x + y = 5 13/5 + y = 5 y = 5 − 𝟏𝟑/𝟓 y = (𝟓(𝟓) − 𝟏𝟑)/𝟓 y = (𝟐𝟓 − 𝟏𝟑)/𝟓 y = 𝟏𝟐/𝟓 Thus, x = 𝟏𝟑/𝟓 , y = 𝟏𝟐/𝟓 Since only one pair of solutions are there ∴ Number of solutions = 1 So, the correct answer is (b)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.