1970 AHSME Problems/Problem 26
Problem
The number of distinct points in the -plane common to the graphs of and is
Solution
The graph of is the union of the lines and (shown in red below). The graph of is the union of the lines and (shown in blue below).
[asy] unitsize(0.8 cm);
draw((-1,0)--(5,0)); draw((0,-1)--(0,5));
draw((0,5)--(5,0),linewidth(1)+red); draw((-1,1)--(5,5),linewidth(1)+red); draw((-1,0)--(4,5),linewidth(1)+blue); draw((2/3,5)--(5,-3/2),linewidth(1)+blue);
label("", (5,0), NE); label("", (0,5), NE);
dot("", (2,3), E); label("", (5,0), E, red); label("", (5,5), E, red); label("", (4,5), N, blue); label("", (5,-3/2), E, blue); [/asy]
https://latex.artofproblemsolving.com/c/w/o/cwocgeak.png?time=1513823210175
Every line passes through the point , so the intersection of the two graphs consists of exactly point. The answer is (B).
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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