Ex 3.7, 7 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 14

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Ex 3.7, 7 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 15

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Ex 3.7, 7 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 16

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

Transcript

Ex 3.7, 7 Solve the following pair of linear equations: (iv) (๐‘Žโˆ’๐‘)๐‘ฅ+(๐‘Ž+๐‘)๐‘ฆ=๐‘Ž2 โˆ’2๐‘Ž๐‘โˆ’๐‘2 (๐‘Ž + b) (x + y) = ๐‘Ž2 + ๐‘2 (a โˆ’ b) ๐‘ฅ + (a + b) y = a2 โˆ’ 2ab โˆ’ b2 โ€ฆ(1) (a + b) (๐‘ฅ + y) = a2 + b2 โ€ฆ(2) Solving equation (2) (a + b) (๐‘ฅ + y) = a2 + b2 (a + b)๐’™ + (a + b)y = a2 + b2 (a + b) y = a2 + b2 โˆ’ (a + b) ๐‘ฅ y = (๐‘Ž^2 + ๐‘^2 โˆ’ (๐‘Ž + ๐‘)๐‘ฅ)/((๐‘Ž + ๐‘)) Putting y = (๐‘Ž^2 + ๐‘^2 โˆ’ (๐‘Ž + ๐‘)๐‘ฅ)/((๐‘Ž + ๐‘)) in equation (1) (a โˆ’ b) ๐‘ฅ + (a + b) y = a2 โˆ’ 2ab โˆ’ b2 (a โˆ’ b) x + (a + b) [(๐‘Ž^2 + ๐‘^2 โˆ’ (๐‘Ž + ๐‘)๐‘ฅ)/((๐’‚ + ๐’ƒ))] = ๐‘Ž2โˆ’2๐‘Ž๐‘โˆ’๐‘2 (a โˆ’ b)x + ๐’‚๐Ÿ + ๐’ƒ๐Ÿ โˆ’ (a + b) x = ๐‘Ž2โˆ’2๐‘Ž๐‘โˆ’๐‘2 ax โˆ’ bx + b2 โˆ’ ax โˆ’ bx = 2๐‘Ž๐‘โˆ’๐‘2 โˆ’ bx โˆ’ bx + b2 = 2๐‘Ž๐‘โˆ’๐‘2 โ€“2bx + b2 = โˆ’2ab โˆ’ b2 โ€“2bx = โˆ’2ab โˆ’ b2 โˆ’ b2 โ€“2bx = โˆ’2ab โˆ’ 2b2 โ€“2bx = โˆ’(2ab + 2b2) 2bx = 2ab + 2b2 2bx = 2b (a + b) x = (2๐‘(๐‘Ž + ๐‘))/2๐‘ x = a + b Put x = a + b in equation (3) y = (๐‘Ž2+ ๐‘2โˆ’ (๐‘Ž + ๐‘)๐‘ฅ)/(๐‘Ž + ๐‘) y = (๐‘Ž2+ ๐‘2 โˆ’ (๐‘Ž + ๐‘)(๐‘Ž + ๐‘))/(๐‘Ž + ๐‘) y = (๐‘Ž2+ ๐‘2 โˆ’ (๐‘Ž + ๐‘)^2)/(๐‘Ž + ๐‘) y = (๐‘Ž2 + ๐‘2 โˆ’ ๐‘Ž2 โˆ’ ๐‘2 โˆ’ 2๐‘Ž๐‘)/(๐‘Ž + ๐‘) y = (โˆ’๐Ÿ๐’‚๐’ƒ)/(๐’‚ + ๐’ƒ) Therefore, x = a + b and y = (โˆ’๐Ÿ๐’‚๐’ƒ)/(๐’‚ + ๐’ƒ).

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.