For what value of k, the system of equations 2/5x+1/ky=4 and 3/5x - 6y =7 will have unique solution?

Question

anonymous · Answer

$$\dfrac{2}{5} x + \dfrac{1}{k} y = 4$$$$\dfrac{3}{5} x - 6y = 7$$---
Do you know the condition for a unique solution?

studystagram · Answer

Yup...I was just confused as to what to do with the 1/ky thing. Should I leave it like that or do i have to simplify or something?

anonymous · Answer

You will have to use that condition. Can you recall what it is?

studystagram · Answer

Yeah I know that...
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anonymous · Answer

Apply the same condition here.

studystagram · Answer

I want to know the answer, dude

anonymous · Answer

Then find it.

studystagram · Answer

That really helps. thanks

anonymous · Answer

$$\large \dfrac{\frac{2}{5}}{\frac{3}{5}}\ne \dfrac{\frac{1}{k}}{-6}$$$$\Rightarrow \dfrac{2}{3} \ne - \dfrac{1}{6k}$$

studystagram · Answer

THIS IS EXACTLY WHERE I WAS CONFUSED. THANK YOU FOR SOLVING!!

anonymous · Answer

Are you being sarcastic?

studystagram · Answer

no lol

anonymous · Answer

One thing is that $k \ne 0$ because you can never divide by zero.  And from the above equation, you will find another value that $k$ cannot hold.

studystagram · Answer

okay. thanks again!