1964 AHSME Problems/Problem 18
Problem 18
Let be the number of pairs of values of and such that and have the same graph. Then is:
Solution
For two lines to be the same, their slopes must be equal and their intercepts must be equal. This is a necessary and sufficient condition.
The slope of the first line is , while the slope of the second line is . Thus, , or .
The intercept of the first line is , while the intercept of the second line is . Thus, , or .
Plugging into gives , or . This means This in turn gives . Thus, , for two solutions, which is answer
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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