Chapter 10 - Section 10.5 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 810: 4

$(x,y)=${$(-6,7),(-2,-1)$}

Re-write the first equation as: $y=-2x-5$ The second equation yields: $-2x-5=x^2+6x+7$ or, $x^2+8x+12=0$ or, $(x+6)(x+2)=0$ or, $x=${$-6,-2$} From first equation when $x=-6$, we have $y=7$ From first equation when $x=-2$, we have $y=-1$ Thus, solution set is $(x,y)=${$(-6,7),(-2,-1)$}