[tex]x-y=14 => x=14+y\\x^2+y^2=116\\\\(14+y)^2+y^2=116\\196+28y+y^2+y^2=116\\2y^2+28y+196=116\\2(y^2+14y+98)=116 /:2\\y^2+14y+98=58\\y^2+14y+40=0\\\Delta=14^2-4*1*40\\\Delta=196-160\\\Delta=36\\\sqrt{\Delta}=6\\y_1=\frac{-14-6}{2}=\frac{-20}2=-10\\y_2=\frac{-14+6}2=\frac{-8}2=-4[/tex]
[tex]x_1=14+y_1\\x_1=14-10\\x_1=4\\\\x_2=14-4\\x_2=10\\\\x_1*y_1=4*(-10)=-40\\x_2*y_2=10*(-4)=-40[/tex]