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: (iii) 4/๐‘ฅ + 3y = 14 3/๐‘ฅ โ€“ 4y = 23 4/๐‘ฅ + 3y = 14 3/๐‘ฅ โ€“ 4y = 23 Let 1/๐‘ฅ = u So, our equations become 4u + 3y = 14 3u โ€“ 4y = 23 Now, our equations are 4u + 3y = 14 โ€ฆ(3) 3u โ€“ 4y = 23 โ€ฆ(4) From (3) 4u + 3y = 14 4u = 14 โ€“ 3y u = (14 โˆ’3๐‘ฆ)/4 Putting value of u in (4) 3u โ€“ 4y = 23 3 ((14 โˆ’ 3๐‘ฆ)/4) โ€“ 4y = 23 Multiplying both sides by 4 4 ร— 3 ((14 โˆ’ 3๐‘ฆ)/4) โ€“ 4 ร— 4y = 4 ร— 23 3(14 โ€“ 3y) โˆ’ 16y = 92 42 โ€“ 9y โˆ’ 16y = 92 โ€“ 9y โ€“ 16y = 92 โ€“ 42 โ€“25y = 50 y = 50/(โˆ’25) y = โ€“ 2 Putting y = โ€“ 2 in equation (3) 4u + 3y = 14 4u + 3(โ€“2) = 14 4u โ€“ 6 = 14 4u = 14 + 6 u = 20/4 u = 5 But u = 1/๐‘ฅ 5 = 1/๐‘ฅ x = ๐Ÿ/๐Ÿ“ Hence, x = ๐Ÿ/๐Ÿ“, y = โ€“2 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: (iv) 5/(๐‘ฅ โˆ’ 1) + 1/(๐‘ฆ โˆ’ 2) = 2 6/(๐‘ฅ โˆ’ 1) โˆ’ 3/(๐‘ฆ โˆ’ 2) = 1 5/(๐‘ฅ โˆ’ 1) + 1/(๐‘ฆ โˆ’ 2) = 2 6/(๐‘ฅ โˆ’ 1) โˆ’ 3/(๐‘ฆ โˆ’ 2) = 1 Let 1/(๐‘ฅ โˆ’ 1) = u & 1/(๐‘ฆโˆ’2) = v So, our equations become 5u + v = 2 6u โ€“ 3v = 1 Our equations are 5u + v = 2 โ€ฆ(3) 6u โ€“ 3v = 1 โ€ฆ(4) From (3) 5u + v = 2 v = 2 โ€“ 5u Putting value of v in (4) 6u โ€“ 3v = 1 6u โ€“ 3(2 โ€“ 5u) = 1 6u โ€“ 6 + 15u = 1 6u + 15u = 1 + 6 21u = 7 u = 7/21 u = ๐Ÿ/๐Ÿ‘ Putting u = 1/3 in (3) 5u + v = 2 5 (1/3) + v = 2 5/3 + v = 2 v = 2 โ€“ 5/3 v = (2(3) โˆ’ 5)/3 v = ๐Ÿ/๐Ÿ‘ Hence, u = 1/3 & v = 1/3 We need to find x & y We know that u = ๐Ÿ/(๐’™ โˆ’ ๐Ÿ) 1/3 = 1/(๐‘ฅ โˆ’ 1) x โ€“ 1 = 3 x = 3 + 1 x = 4 v = ๐Ÿ/(๐’š โˆ’ ๐Ÿ) 1/3 = 1/(๐‘ฆ โˆ’2) y โ€“ 2 = 3 y = 3 + 2 y = 5 So, x = 4, y = 5 is the solution of our equations

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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.