In each of the following cases give an example of a system of two linear equations in two variables $$x$$ and $$y$$.<br>i) A system having exactly one solution<br>ii) A system having no solution<br>iii) A system having infinitely many solutions

PLACEHOLDER ANSWER - the answer is three examples. i) $$x + y = 2$$, $$x - y = 0$$ has exactly one solution, $$x = y = 1$$. ii) $$x + y = 1$$, $$x + y = 2$$ has no solution, since the lines are parallel. iii) $$x + y = 1$$, $$2x + 2y = 2$$ has infinitely many solutions, since both equations describe the same line.