[tex]\left \{ {{x-2y=-1} \atop {xy=1 /:y}} \right. \\\left \{ {{x-2y=-1} \atop {x=\frac1y}} \right. \\\frac1y-2y=-1\\\frac1y-\frac{2y^2}y=-1\\\frac{1-2y^2}y=-1/*y\\1-2y^2=-y\\0=2y^2-y-1\\\Delta=(-1)^2-4*2*(-1)\\\Delta=1+8\\\Delta=9\\\sqrt{\Delta}=\sqrt9=3\\y_1=\frac{1-3}{4}=\frac{-2}4=-\frac12\\y_2=\frac{1+3}4=\frac44=1\\x_1=\frac1{y_1}=1:(-\frac12)=1*(-2)=-2\\x_2=\frac1{y_2}=\frac11=1[/tex]
Rozwiazania:
[tex]x=-2; y=-\frac12 \text{ oraz } x=1; y=1[/tex]
