Last updated at May 19, 2021 by Teachoo

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Ex 3.6, 1 Solve the following pairs of equations by reducing them to a pair of linear equations: (iii) 4/๐ฅ + 3y = 14 3/๐ฅ โ 4y = 23 4/๐ฅ + 3y = 14 3/๐ฅ โ 4y = 23 So, our equations become 4u + 3y = 14 3u โ 4y = 23 Now, our equations are 4u + 3y = 14 โฆ(3) 3u โ 4y = 23 โฆ(4) From (3) 4u + 3y = 14 4u = 14 โ 3y u = (14 โ3๐ฆ)/4 Putting value of u in (4) 3u โ 4y = 23 3 ((14 โ 3๐ฆ)/4) โ 4y = 23 Multiplying both sides by 4 4 ร 3 ((14 โ 3๐ฆ)/4) โ 4 ร 4y = 4 ร 23 3(14 โ 3y) โ 16y = 92 42 โ 9y โ 16y = 92 โ 9y โ 16y = 92 โ 42 โ25y = 50 y = 50/(โ25) y = โ 2 Putting y = โ 2 in equation (3) 4u + 3y = 14 4u + 3(โ2) = 14 4u โ 6 = 14 4u = 14 + 6 u = 20/4 u = 5 But u = 1/๐ฅ 5 = 1/๐ฅ x = ๐/๐ Hence, x = ๐/๐, y = โ2 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/(๐ฅ โ 1) + 1/(๐ฆ โ 2) = 2 6/(๐ฅ โ 1) โ 3/(๐ฆ โ 2) = 1 5/(๐ฅ โ 1) + 1/(๐ฆ โ 2) = 2 6/(๐ฅ โ 1) โ 3/(๐ฆ โ 2) = 1 So, our equations become 5u + v = 2 6u โ 3v = 1 Our equations are 5u + v = 2 โฆ(3) 6u โ 3v = 1 โฆ(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 = ๐/๐ 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) โ 5)/3 v = ๐/๐ Hence, u = 1/3 & v = 1/3 We need to find x & y We know that u = ๐/(๐ โ ๐) 1/3 = 1/(๐ฅ โ 1) x โ 1 = 3 x = 3 + 1 x = 4 v = ๐/(๐ โ ๐) 1/3 = 1/(๐ฆ โ2) y โ 2 = 3 y = 3 + 2 y = 5 So, x = 4, y = 5 is the solution of our equations

About the Author

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.