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99x+101y=499 and 101x+99y=501Solve it?Plz suggest a trick to solve this quickly |
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Answer» Let us use a trick to solve it quickly99x + 101y = 499 ............ i101x + 99y = 501............ iisubtract i from ii2x - 2y = 2 or x - y =1 or x = 1 + y ....... .............................................. iiiadd i and ii200x + 200y = 1000 or x + y = 5 ...................................................................... ivNow from iii and iv , we get 1 + y + y = 5 or 2y = 4 or y = 2 ...... vagain from iii and v , we get x = 1 + 2 = 3Hence x = 3 , y = 2 99x+101y=499 .....(1)101x+99y=501 ......(2)Add (1) and (2), we get200x + 200y = 1000x+y = 5 ...... (3)Subtract (1) from (2), we get2x -2y = 2x - y = 1........ (4)Add (3) and (4), we get2x = 6=> x = 3Put value of x in (3), we get3+y = 5=> y = 2\xa0\xa0\xa0 |
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