1964 AHSME Problems/Problem 19
Contents
Problem 19
If and , the numerical value of is:
Solution 1
If the value of is constant, as the answers imply, we can pick a value of , and then solve the two linear equations for the corresponding . We can then plug in into the expression to get the answer.
If , then and . We can solve each equation for and set them equal, which leads to . This leads to . Plugging in into gives . Thus, is one solution to the intersection of the two planes given.
Plugging into the expression gives gives , or , which is answer
Solution 2
If we think of as a parameter, we get and . Adding the equations leads to , or . Plugging that into gives , or . Thus, the intersection of the two planes is given by the parametric line , where varies along all real numbers.
We plug this in to to get , or , which is answer .
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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