The number of values of `k` for which the system of the equations `(k+1)x+8y=4k` and `k x+(k+3)y=3k-1` has infinitely many solutions is `0` b. `1` c. `2` d. infinite

Options

A. 0
B. 1
C. 2
D. infinite

Answer

B

Explanation

The given system of equations will have infinitely many solutions, if
`|(k +1,8),(k,k +3)| = 0, |(K +1,4k),(k,3k -1)| = 0 and |(4k,8),(3k -1,K +3)| = 0`
`rArr k^(2) - 4k + 3 = 0, -k^(2) + 2k - 1 = 0 and 4k^(2) - 12k + 8 = 0`
`rArr (k-1) (k -3) = 0, (k -1)^(2) = 0, (k-1) (k -2) = 0`
`rArr kk = 1`