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Solve for ` x and y ` : ` ( 3a)/(x) - ( 2b )/(y ) + 5 = 0, (a)/(x) + ( 3b)/( y) - 2 = 0 ( x ne 0 , y ne 0 )` |
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Answer» Putting ` (1)/(x) = u and (1)/(y) = v `, the given equations become ` 3au - 2 bv = - 5" " `… (i) ` au + 3 bv = 2" "`… (ii) Multiplying (ii) by and substracting (i) from the result, we get ` 9bv + 2 bv = 6 + 5` ` rArr 11bv = 11 rArr v = (11)/(11 b ) = (1)/(b)` Putting ` v = (1)/(b) ` in (ii), we get `au + 3= 2 rArr au = - 1 rArr u = (-1)/(a)` Now, `u = (-1)/(a) rArr (1)/(x) = (-1)/(a) rArr - x = a rArr x = - a ` And, ` v = (1)/(b) rArr (1)/(y) = (1)/(b) rArr y = b ` . Hence,` x = - a and y = - b ` |
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