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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 \($(x,y) = (0,0).$ \)

 Jun 18, 2020
 #1
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I'm assuming that you mean "all real constants k"

First add the two equations together. 

\(4(x+y)=k(x+y)\). k = 4

Then subtract the two. 

\(-2(x-y)=k(x-y)\). k = -2.

So our two solutions are k = 4, -2

 Jun 18, 2020

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