Question

Sistema de ecuacion no lineal X+y=1
Xy=-6

Answer 1

$\left \{{x+y=1} \atop {xy=-6}} \right. \; \left \{ {{y=1-x} \atop {x(1-x)=-6}} \right. \; \left \{ {{y=1-x} \atop {x^2-x-6=0}} \right. \; \left \{ {{y=1-x} \atop {x_1=-2\; ,\; x_2=3}} \right. \; \left \{ {{y_1=3\; ,\; y_2=-2} \atop {x_1=-2\; ,\; x_2=3}} \right. \\\\Otvet:\; \; (-2,3)\; ,\; \; (3,-2)\; ,$

Answer 2

$\left \{ {{x+y=1} \atop {xy=6}} \right. \\\left \{ {{xy=-6} \atop {x=1-y}} \right. \\\left \{ {(1){(1-y)*y=-6} \atop {x=1-y}} \right. \\1)(1-y)*y=-6\\y-y^{2} +6=0\\y^{2} -y-6=0\\D=1*1-(-6*4)=25=5^{2} \\Y1=(1+5)/2=3\\Y2=(1-5)/2=-2\\\left \{ {{y=3} \atop {x=-2}} \right. \\\left \{ {{y=-2} \atop {x=3}} \right.$