Question

Реши систему уравнений:

Answer 1

$frac{1}{x+y}=u, frac{1}{x+y}=v;\\left { {{u+v=11} atop {4u+2v=30}} right. \\left { {{v=11-u} atop {4u-2u+22=30}} right. left { {{2u=8} atop {v=11-u}} right. left { {{u=4} atop {v=7}} right. \\left { {{frac{1}{x+y}=4 } atop {frac{1}{x-y}=7 }} right. left { {{x+y=frac{1}{4} } atop {x-y=frac{1}{7} }} right. +\\2x=frac{1}{4}+frac{1}{7}\\2x=frac{11}{28} \\x=frac{11}{56} \frac{11}{56}+y=frac{1}{4}Rightarrow y=frac{1}{4}-frac{11}{56}=frac{3}{56}$

ОТВЕТ: $(frac{11}{56} ;frac{3}{56} )$