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Question

Find the value of k for which the following system of linear equation becomes infinitely many solution or represent the coincident lines.
6x+3y=k3; 2kx+6y=k

A
k = 5
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B
k = 2
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C
k = 6
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D
k = 3
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Solution

The correct option is C k = 6
The given equations are
6x+3y=k3
2kx+6y=k
For infinite solution
a1a2=b1b2=c1c2
we have a1=6.b1=3,c1=k-3
a2=2k,b2=6,c2=k
62k=36=k3k
62k=36
k=6
36=k3k
3k=6k18
3k=18
k=6
For k=6, given system of equation will have infinite sol.

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