The lines (a+2b)x+(a-3b)y=a-b for different values of a and b pass through the fixed point , whose coordinates are

Options

A. `((2)/(5),(2)/(5))`
B. `((3)/(5)(3)/(5))`
C. `((1)/(5),(1)/(5))`
D. `((2)/(5),(3)/(5))`

Answer

D

Explanation

Given equation can be rewritten as `a(x+y-1)+b(2x-3y+1)=0`
This is the form of intersection of two lines.
`thereforex+y-1=0` . . . (i)
and 2x-3y+1=0 . . . (ii)
On solving eqs. ((i) and (ii), we get
`x=(2)/(5) and y=(3)/(5)`
hence, coordinates of required point are `((2)/(5),(3)/(5))`.