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