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Question

Find the value of k for which the following lines intersect,
6x+3y=k3,12x+ky=k

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Solution

6x+3y=k3,12x+ky=k
It has polymony solution
(6x+3y=k3)×212x+6y=2k6(1)
12x+ky=k(2)
Fir the system to be polymony
(1)=(2)
12x+6y2k+6=12x+kyk
On comparing
k=6,2k+6=k
k=6
the value of k=6

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