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Example 17 - Solve: 2/x + 3/y = 13, 5/x - 4/y = -2 - Examples

  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise
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Example 17 Solve the pair of equations: 2/๐‘ฅ+ 3/๐‘ฆ=13 5/๐‘ฅโˆ’4/๐‘ฆ=โˆ’2 2/๐‘ฅ+ 3/๐‘ฆ=13 5/๐‘ฅโˆ’4/๐‘ฆ=โˆ’2 Hence, our equations are 2u + 3v = 13 โ€ฆ(3) 5u โ€“ 4v = โ€“ 2 โ€ฆ(4) From (3) 2u + 3v = 13 2u = 13 โ€“ 3V u = (13 โˆ’ 3๐‘ฃ)/2 Putting value of u (4) 5u โ€“ 4v = - 2 5((13โˆ’3๐‘ฃ)/2)โˆ’4๐‘ฃ=โˆ’2 Multiplying 2 both sides 2 ร— 5((13โˆ’3๐‘ฃ)/2)โˆ’"2 ร—" 4๐‘ฃ="2 ร—"โˆ’2 5(13 โ€“ 3v) โ€“ 8v = โ€“4 65 โ€“ 15v โ€“ 8v = โ€“4 โ€“ 15v โ€“ 8v = โ€“ 4 โ€“ 65 โ€“ 23v = โ€“ 69 v = (โˆ’69)/(โˆ’23) v = 3 Putting v = 3 in (3) 2u + 3v = 13 2u + 3(3) = 13 2u + 9 = 13 2u = 13 โ€“ 9 2u = 4 u = 4/2 u = 2 Hence, u = 2, v = 3 is the solution But we have to find x & y we know that u = 1/๐‘ฅ 2 = 1/๐‘ฅ x = 1/2 Hence, x = 1/2 , y = 1/3 is the solution of the given equation

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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