Chapter 13 - Section 13.3 - Solving Nonlinear Systems of Equations - Exercise Set - Page 948: 29

${(-6, 0), (0,-6), (6,0)}$

$x^2+y^2=36$ $y=1/6*x^2-6$ $y=1/6*x^2-6$ $y+6=1/6*x^2-6+6$ $y+6=1/6*x^2$ $6*(y+6)=6*(1/6*x^2)$ $6y+36=x^2$ $x^2+y^2=36$ $6y+36+y^2=36$ $y^2+6y+36=36$ $y^2+6y+36-36=36-36$ $y^2+6y=0$ $y(y+6)=0$ $y=0$ $y+6=0$ $y+6-6=0-6$ $y=-6$ $y=0$ $y=1/6*x^2-6$ $0=1/6*x^2-6$ $0+6=1/6*x^2-6+6$ $6=1/6*x^2$ $6*6=6*1/6*x^2$ $6^2=x^2$ $\sqrt {6^2} = \sqrt {x^2}$ $x= ±6$ $y=-6$ $y=1/6*x^2-6$ $-6=1/6*x^2-6$ $-6+6=1/6*x^2-6+6$ $0=1/6*x^2$ $0*6=6*1/6*x^2$ $0=x^2$ $\sqrt 0 = \sqrt {x^2}$ $x=0$