Answer
$${\text{The specified points are solution of the nonlinear system of equations}}$$
Work Step by Step
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,\,y = 3{x^2}\,\,\,\left( {\bf{1}} \right) \cr
& {x^2} + {y^2} = 10\,\,\,\,\,\left( {\bf{2}} \right) \cr
& {\text{From the graph we have the solutions }}\left( { - 1,3} \right){\text{ and }}\left( {1,3} \right) \cr
& \cr
& {\text{Evaluate the point }}\left( { - 1,3} \right){\text{ for both equations}} \cr
& y = 3{x^2} \to 3 = 3{\left( { - 1} \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 = 3 \cr
& {x^2} + {y^2} = 10 \to {\left( { - 1} \right)^2} + {\left( 3 \right)^2} = 10 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10 = 10 \cr
& ,{\text{then the point }}\left( { - 1,3} \right){\text{ is a solution of the nonlinear sysyem}} \cr
& \cr
& {\text{Evaluate the point }}\left( {1,3} \right){\text{ for both equations}} \cr
& y = 3{x^2} \to 3 = 3{\left( 1 \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 = 3 \cr
& {x^2} + {y^2} = 10 \to {\left( 1 \right)^2} + {\left( 3 \right)^2} = 10 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10 = 10 \cr
& ,{\text{then the point }}\left( {1,3} \right){\text{ is a solution of the nonlinear sysyem}} \cr} $$
