Last updated at June 22, 2017 by Teachoo

Transcript

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 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 โ3๐ฆ)/4) โ 4y = 23 Multiplying both sides by 4 4 ร 3((14 โ3๐ฆ)/4) โ 4 ร 4y = 4 ร 23 3(14 โ 3y ) - 16y = 92 42 โ 9y - 16y = 92 โ 9y โ 16y = 92 โ 42 โ25y = 50 y = 50/(โ25) = โ 2 Putting y = โ 2 in equation (3) 4u + 3y = 14 4u + 3(โ2) = 14 4u โ 6 = 14 4u = 14 + 6 4u = 20 u = 20/4 u = 5 But u = 1/๐ฅ 5 = 1/๐ฅ x = 1/5 Hence, x = 1/5 , 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 โ1) + 1/(๐ฆ โ2) = 2 6/(๐ฅ โ1) - 3/(๐ฆ โ2) = 1 5/(๐ฅ โ1) + 1/(๐ฆ โ2) = 2 6/(๐ฅ โ1) - 3/(๐ฆ โ2) = 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 = 1/3 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 = (6 โ 5)/3 v = 1/3 Hence, u = 1/3 & v = 1/3 Hence, u = 1/3 & v = 1/3 We need to find x & y We know that 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 9 years. He provides courses for Maths and Science at Teachoo.