Question

Помогите решить систему уравнений

Answer 1

$+\left \{ {{x^{2}-8y+31=0} \atop {y^{2}-2x-14=0 }} \right.\\ --------\\x^{2} -8y+31+y^{2}-2x-14=0\\\\(x^{2}-2x+1)+(y^{2} -8y+16)=0\\\\(x-1)^{2}+(y-4)^{2}=0\\\\(x-1)^{2}=0\\\\x-1=0\\\\x=1\\\\(y-4)^{2}=0\\\\y-4=0\\\\y=4\\\\Otvet:\boxed{(1;4)}$

$+\left \{ {{x^{2}+6y+14=0} \atop {y^{2}+4x-1=0}} \right.\\--------\\x^{2}+6y+14+y^{2}+4x-1=0\\\\(x^{2}+4x+4)+(y^{2}+6y+9)=0\\\\(x+2)^{2}+(y+3)^{2}=0\\\\(x+2)^{2}=0\\\\x+2=0\\\\x=-2\\\\(y+3)^{2}=0\\\\y+3=0\\\\y=-3\\\\Otvet:\boxed{(-2;-3)}$