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What is the solution of the pair of linear equations 37x + 43y = 123, 43x + 37y = 117?

(a) x = 2, y = 1Β  Β  Β (b) x = βˆ’1, y = 2 Β 

(c) x = βˆ’2, y = 1 Β  (d) x = 1, y = 2

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Question 40 What is the solution of the pair of linear equations 37x + 43y = 123, 43x + 37y = 117? (a) x = 2, y = 1 (b) x = βˆ’1, y = 2 (c) x = βˆ’2, y = 1 (d) x = 1, y = 2 Given equations 37π‘₯ + 43𝑦 = 123 …(1) 43π‘₯ + 37𝑦 = 117 …(2) Adding both equations (1) and (2) (37𝒙 + 43π’š) + (43𝒙 + 37π’š) = 123 + 117 (37π‘₯ + 43π‘₯) + (43𝑦 + 37𝑦) = 240 80π‘₯ + 80𝑦 = 240 80(𝒙 + π’š) = 240 π‘₯ + 𝑦 = 240/80 π‘₯ + 𝑦 = 3 Now, subtracting (1) and (2) (37𝒙 + 43π’š) βˆ’ (43𝒙 + 37π’š) = 123 βˆ’ 117 (37π‘₯ βˆ’ 43π‘₯) + (43𝑦 βˆ’ 37𝑦) = 8 βˆ’8π‘₯ + 8𝑦 = 8 8(βˆ’π’™ + π’š) = 8 βˆ’π‘₯ + 𝑦 = 8/8 βˆ’π‘₯ + 𝑦 = 1 Adding (3) and (4) (π‘₯ + 𝑦) + (βˆ’π‘₯ + 𝑦) = 3 + 1 2y = 4 y = 4/2 y = 2 Putting y = 2 in (3) π‘₯ + 𝑦 = 3 π‘₯ + 2 = 3 π‘₯ = 3 βˆ’ 2 π‘₯ = 1 ∴ x = 1, y = 2 So, the correct answer is (d)

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Davneet Singh

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.