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Find all real constants such that the system \begin{align*}
x + 3y &= kx, \\
3x + y &= ky.
\end{align*}
has a solution other than (x,y) = (0,0).$

 Jul 31, 2020
 #1
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The only value is k = 4, because this will lead to x = y (infinitely many solutions).

 Jul 31, 2020

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