Question Number 143240 by cesarL last updated on 11/Jun/21
$$\frac{\mathrm{2}}{{y}}=\frac{\mathrm{1}}{{x}}\left(\frac{{a}}{{y}}+\mathrm{1}\right) \\ $$$${x}=\mathrm{2}\left(\mathrm{4}{a}−{y}\right) \\ $$$${Is}\:{equations}\:{system} \\ $$
Answered by MJS_new last updated on 11/Jun/21
$$\frac{\mathrm{2}}{{y}}=\frac{\mathrm{1}}{{x}}\left(\frac{{a}}{{y}}+\mathrm{1}\right)\:\Leftrightarrow\:\mathrm{2}{x}={a}+{y}\:\Leftrightarrow\:{x}=\frac{{a}+{y}}{\mathrm{2}} \\ $$$$\Rightarrow \\ $$$$\mathrm{2}\left(\mathrm{4}{a}−{y}\right)=\frac{{a}+{y}}{\mathrm{2}} \\ $$$$\mathrm{16}{a}−\mathrm{4}{y}={a}+{y} \\ $$$$\mathrm{15}{a}=\mathrm{5}{y} \\ $$$${y}=\mathrm{3}{a}\:\Rightarrow\:{x}=\mathrm{2}{a} \\ $$