5.12 The roots of the equation $x^{2}-2 x=0$ can be found graphically, that is, equal to finding the x-coordinates of the intersection points of the following sets of equations, with one exception:
(A) $y=x^{2}, y=2 x$.
(B) $y=x^{2}-2 x, y=0$.
(C) $y=x, y=x-2$.
(D) $y=x^{2}-2 x+1, y=1$.
(E) $y=x^{2}-1, y=2 x-1$.
(2nd American High School Mathematics Examination, 1951)
[Solution] The equation $x^{2}-2 x=0$ is equivalent to $x^{2}=2 x$ or $x^{2}-2 x+1=1$ or $x^{2}-1=2 x-1$. Therefore, the answer is $(C)$.