Chapter 7 - Section 7.4 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 850: 16

$(-2,-1)$ or, $(-6,3)$

Here, we have $x=-y-3$ Now, $(-y-3)^2+2y^2=12y+18$ This gives: $3y^2-6y-9=0 $ This yields : $(y+1) (y-3)=0$ when $y=-1$ then we have $x=-(-1)-3=-2$ when $y=3$ then we have $x=-(3)-3=-6$ Hence, our answers are: $(-2,-1)$ or, $(-6,3)$