InterviewSolution
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InterviewSolution
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`1/(2x)-1/y=-1 , 1/x+1/(2y)=8` |
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Answer» The given equations are `(1)/(2x) - (1)/(y) = - 1` ….(1) and `(1)/(x) + (1)/(2y) = 8` …. (2) Let `(1)/(x) = u` and `(1)/(y) = v` then equation (1) and (2) can be written as `(u)/(2) - v = - 1` implies u - 2v = - 2 ….(3) and `u + (v)/(2) = 8` implies 2u + v = 16 .... (4) Multiplying equation (3) by 1 and (4) by 2, we get u - 2v = - 2. ....(5) 4u + 2v = 32 .... (6) Adding equations (5) and (6), we get 5u = 30 implies u = 6 Substituting u = 6 in equation (3), we get 6 - 2v = - 2 implies -2v = - 8 implies v = 4 Now, `(1)/(x) = u` implies `(1)/(x) = 6` implies `x = (1)/(6)` and `(1)/(y) = v` implies `(1)/(y) = 4` implies `y = (1)/(4)` Hence, the solution is `{:(x = (1)/(6)),(y = (1)/(6)):}}` |
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