explain how the solution of a nonlinear system could be just a point ,or two points?

Answer 1

Hi,
Suppose that you have the following two parabolas:
y = x² +1
and
y = -x² +2
Then the parabolas will overlap and thus have two points of intersection.
But suppose that the second equation is changed to
y = -x² +1
Then the curves will touch, be tangent, at (0,1) and, thus, have only one solution.

Hope this helps.
FE.

Answer 2

A simple example is a second order polynomial equation y=ax^2+bx+c ( aparabola) and y=0 (a line) it is a nonlinear system of equation in terms of x because for example doubling x will not double y. The solution can be obtained from ax^2+bx+c=0 with y=0. It
has two real solutions when b^2-4a*c>0,
has one real solution when b^2-4a*c=0 and has no real solution when b^2-4*a*c<0