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Question

Find the value of k for which the system of equations
kxy=2
6x2y=3
has a unique solution?

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Solution

The given system of equations is
kxy2=0
6x2y3=0

It is of the form a1x+b1y+c1=0
a2x+b2y+c2=0,

where a1=k,b1=1,c1=2 and a2=6,b2=2 and c2=3

(i) The given system will have a unique solution, if

a1a2b1b2 i.e, if k612 i.e., k3

So, the given of equations system will have a unique solution, if k3.

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