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The number of values of k, for which the...

The number of values of k, for which the system of equations `(k""+""1)x""+""8y""=""4k` `k x""+""(k""+""3)y""=""3k-1` has no solution, is (1) 1 (2) 2 (3) 3 (4) infinite

A

infinte

B

1

C

2

D

3

Text Solution

Verified by Experts

The given system of equations will have no solution if
`(k+1)/k=8/(k+3) ne (4k)/(3k-1)`
`rArr (k+1)/k=8/(k+3)and 8/(k+3) ne (4k)/(3k-1)`
`rArr k^2 +4k+3=0and 24k-8 ne 4k^2+12k`
`rArr k^2-4k+3=0and 4k^2-12k+8 ne 0`
`rArr k=1,3and k^2-3k+2 ne 0 rArr k=3`
Hence, there is only one value of k.
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