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

Step-by-step solution

Given, equation of line is array rlrl & & (a+2 b) x+(a-3 b) y & =a-b & a x+2 b x+a y-3 b y & =a-b & a(x+y-1)+b(2 x-3 y+1) & =0 array Equating the coefficient, we obtain array r x+y-1=0 2 x-3 y+1=0 array Solve Eqs. (i) and (ii) for x, y , we obtain x=2 / 5, y=3 / 5 Desired point of coordinate is ( 2 5 , 3 5 ) .