Q.

The number of values of k , for which the system of equations  (k+1)x+8y=4k;  kx+(k+3)y=3k−1  has infinitely ,many solutions is

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a

0

b

1

c

2

d

infinite

answer is B.

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Detailed Solution

The given system of equations are (k+1)x+8y=4k  and kx+(k+3)y=3k−1 Given that, the system of equations has infinitely many solutions, Then k+1k=8k+3=4k3k−1 k+1k=4k3k−1     or  8k+3=4k3k−1      After simplification we get k=1
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The number of values of k , for which the system of equations  (k+1)x+8y=4k;  kx+(k+3)y=3k−1  has infinitely ,many solutions is