<<Optimization`UnconstrainedProblems`

funs={
x^2+4y^2-13, x^2-2x y+9y^2-17
};

data=FindRootPlot[funs,{{x,2},{y,3/2}}];

Show[Last[data]]

cp=ContourPlot[Evaluate@Thread[funs==0],{x,-5,5},{y,-5,5}];

cp

Show[{cp,Last[data]}]

data=FindRootPlot[funs,{{x,-.1},{y,0.0001}}];

Show[Last[data]]

Show[{cp,Last[data]}]