Example 18 - Solve 5/x-1 + 1/y-2 = 2, 6/x-1 - 3/y-2 = 1 - Mix questions - Equation given

  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise
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Example 18 Solve the following pair of equations by reducing them to a pair of linear equations : 5/(๐‘ฅ โˆ’1) + 1/(๐‘ฆ โˆ’2) = 2 6/(๐‘ฅ โˆ’1) โ€“ 3/(๐‘ฆ โˆ’2) = 1 5/(๐‘ฅ โˆ’1) + 1/(๐‘ฆ โˆ’2) = 2 6/(๐‘ฅ โˆ’1) โ€“ 3/(๐‘ฆ โˆ’2) = 1 Thus, 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 = 1/3 Putting u = 1/3 in equation (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 = (6 โˆ’ 5)/3 v = 1/3 Hence, u = 1/3 & v = 1/3 But we need to find x & y So, x = 4, y = 5 is the solution of our equations

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