The number of values of `k` for which the lines `(k+1)x+8y=4ka n dk x+(k+3)y=3k-1` are coincident is __________

Answer

1

Explanation

Lines (k+1) x+8y=4k and kx+(k+3)y = 3k-1 are coincident.
Then we can compare the ratio of coefficients as
`(k+1)/(k) = (8)/(k+3) = (4k)/(3k-1)`
`"or " k^(2) +4k +3 = 8k " and " 24k-8=4k^(2) +12k`
or (k-3)(k-1) =0 and (k-2)(k-1)= 0
or k = 1