{1/(x+y)=7,5⇒x+y=2/15⇒x=2/15-y
{1/y-1/x=8⇒x-y=8xy
2/15-2y=8y(2/15-y)
2/15-2y-16y/15+8y²=0
8y²-46y/15+2/15=0
120y²-46y+2=0
D=2116-960=1156
y1=(46-34)/240=1/20⇒x1=2/15-1/20=(8-3)/60=1/12
y2=(46+34)/240=1/3⇒x2=(2/15-1/3=(2-5)/15=-1/5
(1/12;1/20);(-1/5;1/3)