1970 AMC 12 Problem 26
Attempt Problem 26 of the 1970 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1970 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
The number of distinct points in the -plane common to the graphs of and is:
infinite
Answer: B
Small hint:
Each product equation represents a union of two lines
Big hint:
Check the intersection of the two lines in each pair before considering all four pairings
Solution:
The first graph is the union of and those two lines meet at The second graph is the union of and these also meet at In fact, substituting satisfies all four line equations. Since the four lines have distinct slopes, no other point can belong to a line from each graph. There is exactly one common point.
Therefore, the correct answer is B.
Problem 26 in other years
- 1950 AMC 12
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