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Question 40 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

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

(a) x = 2, y = 1     (b) x = −1, y = 2  

(c) x = −2, y = 1   (d) x = 1, y = 2

Transcript

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 = −1, y = 2 (c) x = −2, y = 1 (d) x = 1, y = 2 Given equations 37𝑥 + 43𝑦 = 123 …(1) 43𝑥 + 37𝑦 = 117 …(2) Adding both equations (1) and (2) (37𝒙 + 43𝒚) + (43𝒙 + 37𝒚) = 123 + 117 (37𝑥 + 43𝑥) + (43𝑦 + 37𝑦) = 240 80𝑥 + 80𝑦 = 240 80(𝒙 + 𝒚) = 240 𝑥 + 𝑦 = 240/80 𝑥 + 𝑦 = 3 Now, subtracting (1) and (2) (37𝒙 + 43𝒚) − (43𝒙 + 37𝒚) = 123 − 117 (37𝑥 − 43𝑥) + (43𝑦 − 37𝑦) = 8 −8𝑥 + 8𝑦 = 8 8(−𝒙 + 𝒚) = 8 −𝑥 + 𝑦 = 8/8 −𝑥 + 𝑦 = 1 Adding (3) and (4) (𝑥 + 𝑦) + (−𝑥 + 𝑦) = 3 + 1 2y = 4 y = 4/2 y = 2 Putting y = 2 in (3) 𝑥 + 𝑦 = 3 𝑥 + 2 = 3 𝑥 = 3 − 2 𝑥 = 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo