Difference between revisions of "User:Temperal/Introductory Proportion"

(Problem)
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x=ky
 
x=ky
 
\end{cases} </cmath>
 
\end{cases} </cmath>
Find the possible values of '''k''' in terms of x and y.
+
Find the possible values of '''k''' in terms of '''x''' and '''y'''.
  
 
==Solution==
 
==Solution==

Revision as of 12:32, 22 September 2007

Problem

Suppose $\frac{1}{20}$ is either x or y in the following system: \[\begin{cases} xy=\frac{1}{k}\\ x=ky \end{cases}\] Find the possible values of k in terms of x and y.

Solution

Template:Incomplete If $x=\frac{1} {20}$, then $\frac{y} {20} = \frac{1} {k}$ so $ky=20$ or $ky=\frac{1} {20}$. now we get $k=\frac{20} {y}$ and $\frac{1} {20y}$. If $y=\frac{1} {20}$, then we solve again, we get $k=20x$ and $\frac{20} {x}$