2題 open-ended questions(f2-f3) 15marks

1. No, because we can simply construct a figure with five sides of equal length which is not regular pentagon. One suggestion is as follow:

Construct a square first. Then on one side, construct an equilateral triangle. Then the figure becomes a pentagon, all of the side lengths are equal, but their interior angles are 90, 90, 150, 60 and 150 degrees respectively.


2. If we consider the two linear equations as two straight lines in plane, there are only three cases considering their intersections:
a. they are not parallel and hence intersect at one point
b. they are parallel and hence do not have intersections
c. they are indeed the same line and coincide everywhere and hence have infinitely many intersections.

As we know the intersections are indeed the solutions to the simultaneous linear equation, we can conclude that either the equations have 0, 1 or infinitely many solutions.