Find the value of k for which the systems of equations $5 x - 3 y = 0, 2 x + k y = 0$ has a nonzero solution.

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Solution

The equations $5 x - 3 y = 0, 2 x + k y = 0$

Will have a non zero solution if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$

$5 over 2 equals fraction numerator negative 3 over denominator k end fraction k equals fraction numerator negative 6 over denominator 5 end fraction$

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