Question Number 95966 by i jagooll last updated on 29/May/20
$$\mathrm{find}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{for}\: \\ $$$$\mathrm{xy}+\mathrm{3x}−\mathrm{4y}\:=\:\mathrm{29}\: \\ $$
Answered by john santu last updated on 29/May/20
$$\Rightarrow\mathrm{3}{x}+{xy}−\mathrm{4}{y}−\mathrm{12}\:=\:\mathrm{17}\: \\ $$$$\mathrm{3}\left({x}−\mathrm{4}\right)+{y}\left({x}−\mathrm{4}\right)\:=\:\mathrm{17}\: \\ $$$$\left({x}−\mathrm{4}\right)\left({y}+\mathrm{3}\right)\:=\:\mathrm{17}\: \\ $$$$\left({i}\right)\:{for}\:{x}−\mathrm{4}=\mathrm{1}\:\Rightarrow{y}+\mathrm{3}\:=\:\mathrm{17}\: \\ $$$$\left(\mathrm{5},\mathrm{14}\right) \\ $$$$\left({ii}\right)\:{for}\:{x}−\mathrm{4}=−\mathrm{1}\Rightarrow\mathrm{y}+\mathrm{3}=−\mathrm{17} \\ $$$$\left(\mathrm{3},−\mathrm{20}\right) \\ $$$$\left({iii}\right)\:{for}\:{x}−\mathrm{3}\:=\:\mathrm{17}\:\Rightarrow\mathrm{y}+\mathrm{3}\:=\:\mathrm{1} \\ $$$$\left(\mathrm{20},−\mathrm{2}\right) \\ $$$$\left({iv}\right){for}\:{x}−\mathrm{3}=−\mathrm{17}\Rightarrow\mathrm{y}+\mathrm{3}=−\mathrm{1} \\ $$$$\left(−\mathrm{14},\:−\mathrm{4}\right)\: \\ $$
Commented by i jagooll last updated on 29/May/20
$$\mathrm{thank}\:\mathrm{you} \\ $$
Commented by Rasheed.Sindhi last updated on 29/May/20
$$\mathcal{C}{ooool}! \\ $$
Commented by john santu last updated on 29/May/20
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Commented by mr W last updated on 29/May/20
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