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# help due on in an hour

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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

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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