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Find the ordered pair (m,n) where m,n are positive integers satisfying the following equation:

14mn = 55 - 7m - 2n

Please put the answer and explain why.

(I don't really get how to facor 55-2n into the form of **x(2n + 1)**)

Guest May 13, 2018

#1**+1 **

14mn = 55 - 7m - 2n

Add 2n to both sides:

14mn + 2n = 55 - 7m

Factor:

n(14m + 2) = 55 - 7m

Divide both sides by 14m + 2:

n = (55 - 7m) / (14m + 2)

If you replace m with 1: (a guess; if it doesn't work, try 2 ... )

n = (55 - 7·1) / (14·1 + 2) = (55 - 7) / (14 + 2) = 48 / 16 = 3

If m = 1, then n = 3

geno3141 May 13, 2018