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 $\boxed{\textbf{(C)}}$.

See Also

1951 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 32
Followed by
Problem 34
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