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Solove-for-x-and-y-2-x-3-y-31-eauation-i-3-x-2-y-17-equation-ii-please-help-




Question Number 5920 by sanusihammed last updated on 05/Jun/16
Solove for x and y    2^x  + 3^y  = 31   ............ eauation (i)  3^x  + 2^(y )  = 17  ............ equation (ii)    please help.
$${Solove}\:{for}\:{x}\:{and}\:{y} \\ $$$$ \\ $$$$\mathrm{2}^{{x}} \:+\:\mathrm{3}^{{y}} \:=\:\mathrm{31}\:\:\:…………\:{eauation}\:\left({i}\right) \\ $$$$\mathrm{3}^{{x}} \:+\:\mathrm{2}^{{y}\:} \:=\:\mathrm{17}\:\:…………\:{equation}\:\left({ii}\right) \\ $$$$ \\ $$$${please}\:{help}. \\ $$$$ \\ $$
Commented by FilupSmith last updated on 05/Jun/16
2^x +3^y −31=3^x +2^y −17  2^x −2^y +3^y −3^x =14  2^x −3^x −2^y +3^y =14
$$\mathrm{2}^{{x}} +\mathrm{3}^{{y}} −\mathrm{31}=\mathrm{3}^{{x}} +\mathrm{2}^{{y}} −\mathrm{17} \\ $$$$\mathrm{2}^{{x}} −\mathrm{2}^{{y}} +\mathrm{3}^{{y}} −\mathrm{3}^{{x}} =\mathrm{14} \\ $$$$\mathrm{2}^{{x}} −\mathrm{3}^{{x}} −\mathrm{2}^{{y}} +\mathrm{3}^{{y}} =\mathrm{14} \\ $$

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