Chapter 13 - Section 13.3 - Solving Nonlinear Systems of Equations - Exercise Set - Page 948: 10

${(-2, -i), (-2, i), (2, -i), (2, i)}$

$x^2+2y^2=2$ $x^2-2y^2=6$ $x^2+2y^2+(x^2-2y^2)=2+6$ $x^2+2y^2+x^2-2y^2=8$ $2x^2=8$ $2x^2/2=8/2$ $x^2=4$ $\sqrt {x^2} =\sqrt 4$ $x= ±2$ $x^2+2y^2=2$ $4+2y^2=2$ $4+2y^2-4=2-4$ $2y^2=-2$ $2y^2/2=-2/2$ $y^2=-1$ $\sqrt {y^2} =\sqrt {-1}$ $y=±i$