Which-of-the-following-linear-diophantine-equations-has-positive-solutions-A-x-5y-7-B-x-5y-3-B-x-5y-2-C-x-5y-1-

Question Number 145336 by physicstutes last updated on 04/Jul/21

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{linear}\:\mathrm{diophantine}\:\mathrm{equations}\:\mathrm{has} \\ $$$$\mathrm{positive}\:\mathrm{solutions}, \\ $$$$\mathrm{A}.\:{x}+\:\mathrm{5}{y}\:=\:\mathrm{7} \\ $$$$\mathrm{B}.\:{x}+\mathrm{5}{y}\:=\:\mathrm{3} \\ $$$$\mathrm{B}.\:{x}\:+\:\mathrm{5}{y}\:=\:\mathrm{2} \\ $$$$\mathrm{C}.\:{x}+\:\mathrm{5}{y}\:=\:\mathrm{1} \\ $$

Commented by Rasheed.Sindhi last updated on 04/Jul/21

$$\mathrm{A}.\:{x}+\:\mathrm{5}{y}\:=\:\mathrm{7} \\ $$

Commented by physicstutes last updated on 04/Jul/21

$$\mathrm{Please}\:\mathrm{sir}\:\mathrm{is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{quik}\:\mathrm{way}\:\mathrm{to}\:\mathrm{figure}\:\mathrm{that}\:\mathrm{out}? \\ $$

Commented by mr W last updated on 04/Jul/21

$${x}\geqslant\mathrm{1},\:{y}\geqslant\mathrm{1} \\ $$$${x}+\mathrm{5}{y}\geqslant\mathrm{1}+\mathrm{5}×\mathrm{1}=\mathrm{6} \\ $$$$\Rightarrow{only}\:{x}+\mathrm{5}{y}=\mathrm{7}\:{fulfills}\:{this}! \\ $$

Commented by physicstutes last updated on 04/Jul/21

$$\mathrm{wow}\:\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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