The number of values of `k` for which the system of equations:
`kx+(3k+2)y=4k`
`(3k-1)x+(9k+1)y=4(k+1)` has no solution, are

Options

A. infinite
B. 1
C. 2
D. 3

Answer

2

Explanation

`Delta = |{:(k+1,,8),(k,,k+3):}|= k^(2) +4k +3 -8k`
`=k^(2) -4k +3`
`=(k-3) (k-1)`
`Delta_(1) = |{:(4k,,8),(3k,,k+3):}| = 4k^(3) +12k -24k+8`
`=4k^(2) -12k +8`
`=4(k^(2)-3k+2)`
`=4(k-2)(k-1)`
`Delta_(2)= |{:(k+1,,4k),(k,,3k-1):}| =3k^(2) +2k -1 -4k^(2)`
`=-k^(2) +2k -1`
`=-(k-1)^(2)`
As given no solution
`rArr k=3` for which `Delta =0 ` and `Delta_(1),Delta_(2) , ne 0`