1951 AHSME Problems/Problem 33

Problem

The roots of the equation $x^{2}-2x = 0$ can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair:

$\textbf{(A)}\ y = x^{2}, y = 2x\qquad\textbf{(B)}\ y = x^{2}-2x, y = 0\qquad\textbf{(C)}\ y = x, y = x-2\qquad\textbf{(D)}\ y = x^{2}-2x+1, y = 1$ $\textbf{(E)}\ y = x^{2}-1, y = 2x-1$

[Note: Abscissas means x-coordinate.]

Solution

If you find the intersections of the curves listed in the answers $\textbf{(A)}$ , $\textbf{(B)}$ , $\textbf{(D)}$ , and $\textbf{(E)}$ , you will find that their abscissas are $0$ and $2$ . Also you can note that the curves in $\textbf{(C)}$ don't actually intersect. Therefore the answer is $\boxed{\textbf{(C)}}$ .

1951 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 32	Followed by Problem 34
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1951 AHSME Problems/Problem 33

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