The number of values of c, for which the system of equation `(c+1)x+8y=4c, cx + (c +3)y= 3c-1` has no solution is :

Options

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

Answer

B

Explanation

`Delta = |{:(c+1 , 8),(c, c+3):}| = c^2 + 4c + 3 - 8c`
`=c^2 - 4c + 3 =(c-3)(c-1)`
`Delta_1 = |{:(4c, 8),(3c-1, c+3):}| = 4c^2 + 12c - 24c + 8`
`= 4c^2 - 12 c + 8 = 4(c^2 - 3c +2)`
`4(c-2)(c-1)`
`Delta_2 =|{:(c+1 , 4c),(c, 3c-1):}|= 3c^2 + 12c -1 - 4c^2`
`=-c^2 + 2c -1 =-(c-1)^2` as given no solution
`implies Delta_1 and Delta_2 ne 0`
But `Delta =0 implies c=3`