Chapter 10 - Section 10.3 - Solving Nonlinear Systems of Equations - Exercise Set - Page 625: 46

$2$ and $4$, $-2$ and $-4$

$x^2+y^2=20$ $xy=8$ $xy=8$ $xy/y=8/y$ $x=8/y$ $x^2+y^2=20$ $(8/y)^2 +y^2=20$ $64/y^2+y^2=20$ $y^2=w$ $64/y^2+y^2=20$ $64/w+w=20$ $w(64/w+w)=20*w$ $64+w^2=20w$ $w^2+64-20w=20w-20w$ $w^2-20w+64=0$ $(w-4)(w-16)=0$ $y^2=w$ $(w-4)(w-16)=0$ $(y^2-4)(y^2-16)=0$ $(y+2)(y-2)(y+4)(y-4)=0$ $y+2=0$ $y+2-2=0-2$ $y=-2$ $y-2=0$ $y-2+2=0+2$ $y=2$ $y+4=0$ $y+4-4=0-4$ $y=-4$ $y-4=0$ $y-4+4=0+4$ $y=4$