Question

5/X+Y -2/X-Y =1,15/X+Y + 7/X-Y =10

Answer 1

Answer:

$\frac{5}{x+y}-\frac{2}{x-y}=1...(1)\\\\\frac{15}{x+y}+\frac{7}{x-y}=10...(2)$

substracting 3*(1) from (2) , we get,

$\frac{15}{x+y}+\frac{7}{x-y}-(\frac{15}{x+y} -\frac{6}{x-y} )=10-3\\\\=>\frac{13}{x-y}=7\\\\ =>x=y+\frac{13}{7}...(3)$

Sub. (3) in (1) , we get ,

$\geq \frac{5}{y+\frac{13}{7}+y } -\frac{2}{y+\frac{13}{7}-y} =1\\\\=>\frac{35}{14y+13}-\frac{14}{13}=1\\\\ =>\frac{35}{14y}=\frac{27}{13} \\\\=>\frac{5}{2y}=\frac{27}{13}\\\\ =>y=\frac{65}{54}$

sub. $y=\frac{65}{54}$ in (3) , we get ,

$x=\frac{65}{54}+\frac{13}{7} \\\\=>x=\frac{455+702}{378}\\\\=>x=\frac{1157}{378}$

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