Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10

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  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise

Transcript

Ex 3.6, 1 Solve the following pairs of equations by reducing them to a pair of linear equations: (i) 1/2๐‘ฅ + 1/3๐‘ฆ = 2 1/3๐‘ฅ + 1/2๐‘ฆ = 13/6 1/2๐‘ฅ + 1/3๐‘ฆ = 2 1/3๐‘ฅ + 1/2๐‘ฆ = 13/6 Let 1/๐‘ฅ = u 1/๐‘ฆ = v So, our equations become 1/2 u + 1/3 v = 2 (3๐‘ข + 2๐‘ฃ)/(2 ร— 3) = 2 3u + 2v = 12 1/3 u + 1/2 v = 13/6 (2๐‘ข +3๐‘ฃ)/(2 ร— 3) = 13/6 2u + 3v = 13 Our equations are 3u + 2v = 12 โ€ฆ(3) 2u + 3v = 13 โ€ฆ(4) From (3) 3u + 2v = 12 3u = 12 โ€“ 2v u = (12 โˆ’ 2๐‘ฃ)/3 Putting value of u in (4) 2u + 3v = 13 2 ((12 โˆ’2๐‘ฃ)/3) + 3v = 13 Multiplying both sides by 3 3 ร— 2((12 โˆ’ 2๐‘ฃ)/3) + 3 ร— 3v = 3 ร— 13 2(12 โ€“ 2v) + 9v = 39 24 โ€“ 4v + 9v = 39 โ€“ 4v + 9v = 39 โ€“ 24 5v = 15 v = 15/5 v = 3 Putting v = 3 in (3) 3u + 2v = 12 3u + 2(3) = 12 3u + 6 = 12 3u = 12 โ€“ 6 3u = 6 u = 6/3 u = 2 Hence, v = 3, u = 2 But we have to find x & y We know that u = ๐Ÿ/๐’™ 2 = 1/๐‘ฅ x = ๐Ÿ/๐Ÿ v = ๐Ÿ/๐’š 3 = 1/๐‘ฆ y = ๐Ÿ/๐Ÿ‘ So, x = ๐Ÿ/๐Ÿ , y = ๐Ÿ/๐Ÿ‘ is the solution of the given equation Ex 3.6, 1 Solve the following pairs of equations by reducing them to a pair of linear equations: (ii) 2/โˆš๐‘ฅ + 3/โˆš๐‘ฆ = 2 4/โˆš๐‘ฅ โˆ’ 9/โˆš๐‘ฆ = โ€“1 2/โˆš๐‘ฅ + 3/โˆš๐‘ฆ = 2 4/โˆš๐‘ฅ โˆ’ 9/โˆš๐‘ฆ = โˆ’1 Let 1/โˆš๐‘ฅ = u & 1/โˆš๐‘ฆ = v So, our equations become 2u + 3v = 2 4u โ€“ 9v = โ€“1 Our equations 2u + 3v = 2 โ€ฆ(3) 4u โ€“ 9v = โ€“1 โ€ฆ(4) From (3) 2u + 3v = 2 2u = 2 โ€“ 3v u = (2 โˆ’ 3๐‘ฃ)/2 Putting value of u in (4) 4u โ€“ 9v = โ€“ 1 4 ((2 โˆ’ 3๐‘ฃ)/2) โ€“ 9v = โ€“1 2(2 โ€“ 3v) โ€“ 9v = โ€“1 4 โ€“ 6v โ€“ 9v = โ€“1 โ€“ 6v โ€“ 9v = โ€“1 โ€“ 4 โ€“15v = โ€“ 5 v = (โˆ’5)/(โˆ’15) v = ๐Ÿ/๐Ÿ‘ Putting v = 1/3 in (3) 2u + 3v = 2 2u + 3 (1/3) = 2 2u + 1 = 2 2u = 2 โ€“ 1 u = ๐Ÿ/๐Ÿ Hence, u = 1/2 & v = 1/3 But, we need to find x & y u = ๐Ÿ/โˆš๐’™ 1/2 = 1/โˆš๐‘ฅ โˆš๐‘ฅ = 2 Squaring both sides (โˆš๐‘ฅ)2 = (2)2 x = 4 v = ๐Ÿ/โˆš๐’š 1/3 = 1/โˆš๐‘ฆ โˆš๐‘ฆ = 3 Squaring both sides (โˆš๐‘ฆ)2 = (3)2 y = 9 Therefore, x = 4, y = 9 is the solution of the given equation

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.