[tex]\left \{ {{\frac{x}{y}+\frac{y}{x}=2 } \atop {x+y=2}} \right.\\\\\left \{ {{\frac{x^2+y^2}{x*y}=2 } \atop {x+y=2}} \right. \\\\\left \{ {{\frac{(x+y)^2-2*x*y}{x*y}=2 } \atop {x+y}=2} \right. \\\left \{ {{4-4x*y=0} \atop {x+y=2}} \right. \\\\\left \{ {{x*y=1} \atop {x+y=2}} \right. \\\\\left \{ {{y(2-y)-1=0} \atop {x=2-y}} \right. \\\left \{ {{y^2-2*y+1=0} \atop {x=2-y}} \right. \\\left \{ {{(y-1)^2=0} \atop {x=2-y}} \right. \\\left \{ {{y=1} \atop {x=1}} \right. \\Bafta![/tex]
