9superb Q
a must try for every aspirant
Prove that 2x+3y and 9x+5y are divisible by 17 for the same set of integers x,y
(A bit easy, so plz give newcomers some time to have a go)
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6 Answers
106So 17k (k is an integer) = 2(k+3l) + 3(5k-2l) [ by observation]
So, x = k+3l and y = 5k-2l
So, 9x + 5y = 9(k+3l) + 5(5k-2l)
= 34k + 17l = 17(2k+l) = 17m
Hence Proved
341thats nice
another way is to note that 7(9x+5y) - 6(2x+3y) = 17(3x+y)
So if one of the expressions is divisible by 17, so is the other.
9nice method :)
mine was diff
2x + 3y = α
9x + 5y = β
now 3β = 17x + 5α
so β is multiple of 17 iff α is multiple of 17
hence proved
399(2x+3y)-2(9x+5y) = something obviously divisible by 17
9,2 are coprime to 17
hence proved