Chapter 13 - Section 13.3 - Solving Nonlinear Systems of Equations - Exercise Set - Page 948: 19

${(-1, -2), (-1,2), (1,-2), (1,2)}$

$2x^2+3y^2=14$ $-x^2+y^2=3$ $-x^2+y^2=3$ $2*(-x^2+y^2=3)$ $-2x^2+2y^2=6$ $2x^2+3y^2=14$ $-2x^2+2y^2=6$ $2x^2+3y^2+(-2x^2+2y^2)=14+6$ $2x^2+3y^2-2x^2+2y^2=20$ $5y^2=20$ $5y^2/5=20/5$ $y^2=4$ $\sqrt {y^2} =\sqrt 4$ $y=±2$ $2x^2+3y^2=14$ $2x^2+3*4=14$ $2x^2+12=14$ $2x^2+12-12=14-12$ $2x^2=2$ $2x^2/2=2/2$ $x^2=1$ $\sqrt {x^2} =sqrt 1$ $x=±1$