Answer
$${\text{The specified points are solution of the nonlinear system of equations}}$$
Work Step by Step
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,\,y = - \frac{4}{9}{x^2}\,\,\,\left( {\bf{1}} \right) \cr
& {x^2} + {y^2} = 25\,\,\,\,\,\,\,\,\,\,\left( {\bf{2}} \right) \cr
& {\text{From the graph we have the solutions }}\left( { - 3, - 4} \right){\text{ and }}\left( {3, - 4} \right) \cr
& \cr
& {\text{Evaluate the point }}\left( { - 3, - 4} \right){\text{ for both equations}} \cr
& y = - \frac{4}{9}{x^2} \to - 4 = - \frac{4}{9}{\left( { - 3} \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 4 = - 4 \cr
& {x^2} + {y^2} = 25 \to {\left( { - 3} \right)^2} + {\left( { - 4} \right)^2} = 25 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,25 = 25 \cr
& ,{\text{then the point }}\left( { - 3, - 4} \right){\text{ is a solution of the nonlinear sysyem}} \cr
& \cr
& y = - \frac{4}{9}{x^2} \to - 4 = - \frac{4}{9}{\left( { - 3} \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 4 = - 4 \cr
& {x^2} + {y^2} = 25 \to {\left( 3 \right)^2} + {\left( { - 4} \right)^2} = 25 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,25 = 25 \cr
& ,{\text{then the point }}\left( {3, - 4} \right){\text{ is a solution of the nonlinear sysyem}} \cr} $$
