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Ex 3.6, 1 (i) and (ii) - Solve 1/2x + 1/3y = 2 , 1/3x +1/2y - Mix questions - Equation given

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Ex 3.6 , 1 Solve the following pairs of equations by reducing them to a pair of linear equations: (i) 1/2๐‘ฅ + 1/3๐‘ฆ = 2 1/3๐‘ฅ + 1/2๐‘ฆ = 13/6 1/2๐‘ฅ + 1/3๐‘ฆ = 2 1/3๐‘ฅ + 1/2๐‘ฆ = 13/6 So, our equations become Our equations are 3u + 2v = 12 โ€ฆ(3) 2u + 3v = 13 โ€ฆ(4) From (3) 3u + 2v = 12 3u = 12 โ€“ 2v u = (12 โˆ’2๐‘ฃ)/3 Putting value of u in (4) 2u + 3v = 13 2((12 โˆ’2๐‘ฃ)/3) + 3v = 13 Multiplying both sides by 3 3 ร— 2((12 โˆ’2๐‘ฃ)/3) + 3 ร— 3v = 3 ร— 13 2(12 โ€“ 2v) + 9v = 39 24 โ€“ 4v + 9v = 39 โ€“ 4v + 9v = 39 โ€“ 24 5v = 15 v = 15/5 v = 3 Putting v = 3 in (3) 3u + 2v = 12 3u + 2(3) = 12 3u + 6 = 12 3u = 12 โ€“ 6 3u = 6 u = 6/3 u = 2 Hence v = 3, u = 2 But we have to find x & y We know that So, x = 1/2 , y = 1/3 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: (ii) 2/โˆš๐‘ฅ + 3/โˆš๐‘ฆ = 2 4/โˆš๐‘ฅ โˆ’ 9/โˆš๐‘ฆ = โ€“1 2/โˆš๐‘ฅ + 3/โˆš๐‘ฆ = 2 4/โˆš๐‘ฅ โˆ’ 9/โˆš๐‘ฆ = -1 Our equations 2u + 3v = 2 โ€ฆ(3) 4u โ€“ 9v = โ€“1 โ€ฆ(4) From (3) 2u + 3v = 2 2u = 2 โ€“ 3v u = (2 โˆ’3๐‘ฃ)/2 Putting value of u in (4) 4u โ€“ 9v = โ€“ 1 4((2 โˆ’3๐‘ฃ)/2) โ€“ 9v = โ€“ 1 2(2 โ€“ 3v) โ€“ 9v = โ€“ 1 4 โ€“ 6v โ€“ 9v = โ€“ 1 โ€“ 6v โ€“ 9v = โ€“ 1 โ€“ 4 โ€“ 15v = โ€“ 5 v = (โˆ’5)/(โˆ’15) v = 1/3 Putting v = 1/3 in (3) 2u + 3v = 2 2u + 3(1/3) = 2 2u + 1 = 2 2u = 2 โ€“ 1 2u = 1 u = 1/2 Hence u = 1/2 & v = 1/3 But, we need to find x & y We need to find x & y Therefore, x = 4, y = 9 is the solution of the given equation

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