Chapter 7 - Section 7.4 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 850: 4

$(-2,-1)$ or $(-6,7)$

Here, we have $y=x^2+6x+7$ Now, $2x+(x^2+6x+7)=-5$ This gives: $x^2+8x+12=0$ This yields : $(x+2)(x+6)=0$ when $x=-2$ then we have $y=(-2)^2+6(-2)+7=-1$ and when $x=-6$ then we have $y=(-6)^2+6(6)+7=7$ Hence, our answers are: $(-2,-1)$ or $(-6,7)$