Chapter 10 - Section 10.5 - Systems of Nonlinear Equations in Two Variables - Exercise Set - Page 811: 50

{$(-5,0),(-3,18),(3,72)$}

Re-write the first equation as: $y=9x+45$ Second equation yields: $9x+45=x^3+5x^2$ or, $x^3+5x^2-9x-45=0$ or,$(x+5)(x^2-9)=0$ or, $x=${$-5,-3,3$} From first equation $-9x+y=45$ when $x=-5$, we have $y=0$ From first equation $-9x+y=45$ when $x=-3$, we have $y=18$ From first equation $-9x+y=45$ when $x=3$, we have $y=72$ Thus, solution set is: {$(-5,0),(-3,18),(3,72)$}