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
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Last updated at Sept. 9, 2021 by Teachoo
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 = โ1, y = 2 (c) x = โ2, y = 1 (d) x = 1, y = 2 Given equations 37๐ฅ + 43๐ฆ = 123 โฆ(1) 43๐ฅ + 37๐ฆ = 117 โฆ(2) Adding both equations (1) and (2) (37๐ + 43๐) + (43๐ + 37๐) = 123 + 117 (37๐ฅ + 43๐ฅ) + (43๐ฆ + 37๐ฆ) = 240 80๐ฅ + 80๐ฆ = 240 80(๐ + ๐) = 240 ๐ฅ + ๐ฆ = 240/80 ๐ฅ + ๐ฆ = 3 Now, subtracting (1) and (2) (37๐ + 43๐) โ (43๐ + 37๐) = 123 โ 117 (37๐ฅ โ 43๐ฅ) + (43๐ฆ โ 37๐ฆ) = 8 โ8๐ฅ + 8๐ฆ = 8 8(โ๐ + ๐) = 8 โ๐ฅ + ๐ฆ = 8/8 โ๐ฅ + ๐ฆ = 1 Adding (3) and (4) (๐ฅ + ๐ฆ) + (โ๐ฅ + ๐ฆ) = 3 + 1 2y = 4 y = 4/2 y = 2 Putting y = 2 in (3) ๐ฅ + ๐ฆ = 3 ๐ฅ + 2 = 3 ๐ฅ = 3 โ 2 ๐ฅ = 1 โด x = 1, y = 2 So, the correct answer is (d)
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [MCQ]
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