Розвязати систему рівняньх/у+у/х=5/2    х+у=3

[latex] \left \{ {{ \frac{x}{y} + \frac{y}{x} = \frac{5}{2} } \atop {x+y=3}} \right. \\ \left \{ {{ \frac{3-y}{y}+ \frac{y}{3-y}= \frac{5}{2} } \atop {x=3-y}} \right. \\ \left \{ {{ \frac{3y-y^2+3y-y^2}{y(3-y)}=2,5 } \atop {x=3-y}} \right. \\ \left \{ {{ \frac{6y-2y^2}{y(3-y)}=2,5 } \atop {x=3-y}} \right. \\ \left \{ {{ \frac{6-2y}{3-y}=2.5 } \atop {x=3-y}} \right. \\ \left \{ {{6-2y-2.5(3-y)=0} \atop {x=3-y}} \right. \\ \left \{ {{6-2y-7.5+2.5y=0} \atop {x=3-y}} \right.[/latex] [latex] \left \{ {{0.5y=1.5} \atop {x=3-y}} \right. \\ \left \{ {{y= \frac{1.5}{0.5}=3 } \atop {x=3-3=0}} \right. [/latex]