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Question

Find the value of k for which the following system of equations has a unique solution:
kx+3y=(k3),12x+ky=k.

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Solution

kx+3y=(k3),12x+ky=k.

Here,
a1=k,b1=3,c1=k3
a2=12,b2=k,c2=k

a1a2b1b2k123k
System has unique solution.

k236k±36
k±6
k is not equal to 6 or 6.

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