1970 AHSME Problems/Problem 26
Contents
[hide]Problem
The number of distinct points in the -plane common to the graphs of and is
Solution 1
The graph is the combined graphs of and . Likewise, the graph is the combined graphs of and . All these lines intersect at one point, . Therefore, the answer is .
Solution 2
We need to satisfy both and . In order to do this, let us look at the first equation. Either or For the second equation, either or Thus, we need to solve 4 systems of equations: and , and , and , and finally and Solving all of these systems of equations is pretty trivial, and all of them come out to be Thus, they only intersect at point, and our answer is .
~SirAppel
See also
1970 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 25 |
Followed by Problem 27 | |
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