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

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Ex 3.7, 7 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 11

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Ex 3.7, 7 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 12 Ex 3.7, 7 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 13

 

  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: (iii) ๐‘ฅ/๐‘Ž โ€“ ๐‘ฆ/๐‘ = 0 ax + by = a2 + b2 ๐‘ฅ/๐‘Ž โˆ’ ๐‘ฆ/๐‘ = 0 โ€ฆ(1) ax + by = ๐‘Ž2+๐‘2 โ€ฆ(2) Solving Equation (1) ๐‘ฅ/๐‘Ž โˆ’ ๐‘ฆ/๐‘ = 0 (๐‘๐‘ฅ โˆ’ ๐‘Ž๐‘ฆ)/๐‘Ž๐‘ = 0 bx โˆ’ ay = 0 Now, solving equations (2) & (3) bx โˆ’ ay = 0 Multiplying both sides by b b(bx โ€“ ay) = b ร— 0 b2x โˆ’ aby = 0 ax + by = a2 + b2 Multiplying both sides by a a(ax + by) = a(a2 + b2) a2x + aby = a3 + ab2 Hence, our equations are b2x โˆ’ aby = 0 โ€ฆ(4) a2x + aby = a3 + ab2 โ€ฆ(5) From equation (4) b2x โˆ’ aby = 0 b2x = aby aby = b2x y = (๐‘^2 ๐‘ฅ)/๐‘Ž๐‘ y = ๐‘๐‘ฅ/๐‘Ž Putting y = ๐‘๐‘ฅ/๐‘Ž in equation (5) a2x + aby = a3 + ab2 a2๐‘ฅ + ab(๐‘๐‘ฅ/๐‘Ž) = a3 + ab2 a2๐‘ฅ + b2๐‘ฅ = a3 + ab2 (a2 + b2) ๐‘ฅ = a (a2 + b2) ๐‘ฅ = (๐‘Ž(๐‘Ž^2 + ๐‘^2))/((๐‘Ž^2 + ๐‘^2)) ๐’™ = a Putting ๐‘ฅ = a in equation (4) b2๐‘ฅ โˆ’ aby = 0 b2(a) โˆ’ aby = 0 ab2 โˆ’ aby = 0 ab2 = aby aby = ab2 y = (๐‘Ž๐‘^2)/๐‘Ž๐‘ y = b Therefore, ๐’™ = a and y = b

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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.