Difference between revisions of "2002 AMC 10B Problems/Problem 13"
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== Solution 2 == | == Solution 2 == | ||
| − | Since we want only the <math>y</math>-variable to be present, we move the terms only with the <math>y</math>-variable to one side, thus constructing <math>8xy - 12y + 2x - 3 = 0</math> to | + | Since we want only the <math>y</math>-variable to be present, we move the terms only with the <math>y</math>-variable to one side, thus constructing <math>8xy - 12y + 2x - 3 = 0</math> to <math>8xy + 2x = 12y + 3</math>. For there to be infinite solutions for <math>y</math> and there is no <math>x</math>, we simply find a value of <math>x</math> such that the equation is symmetrical. |
== See Also == | == See Also == | ||
Revision as of 12:07, 30 November 2019
Contents
Problem
Find the value(s) of 
such that 
is true for all values of 
.
Solution
We have 
.
As 
must be true for all , we must have 
, hence 
.
Solution 2
Since we want only the -variable to be present, we move the terms only with the -variable to one side, thus constructing to 
. For there to be infinite solutions for and there is no , we simply find a value of such that the equation is symmetrical.
See Also
| 2002 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
