For each part below, give an example of a linear system of
equations in two variables that has the given property. In each case, draw the lines
corresponding to the solutions of the equations in the system.
(a) has no solution
(b) has exactly one solution
(c) has infinitely many solutions
(i) Add or remove equations in (b) to make an inconsistent system.
(ii) Add or remove equations in (b) to create infinitely many solutions.
(iii) Add or remove equations in (b) so that the solution space remains unchanged.
(iv) Can you add or remove equations in (b) to change the unique solution you had
to a different unique solution?
In each of (i) - (iv) justify your action in words.