Newton

>

> eqns:={y-x^3,3*y-x-1};
vars:={x,y};
plot({x^(1/3),(x+1)/3},x=0..0.1);
sols:=solve({y-x^3=0,3*y-x-1=0},{x,y});

> solve({-1.08*x+y=-0.084,-x+3*y=0.7},{x,y});

> solve({-2.851875*x+y=0.201859375,-x+3*y=-0.2},{x,y});

> solve({-1.08*x+y=-0.432,-x+3*y=1.0},{x,y});

> solve({-3.151875*x+y=-2.15378125,-x+3*y=1.0},{x,y});

>