min. (a+b) = 56

No I'm also getting 7.

a+11b = k(13)

a+13b= k'(11)

(a+11b) + 2b =k'(11)

b = k'(11) - k(13) (but b>0)  => b = 9/2 and therefore, a = 5/2

Hence a + b = 7

Ques> If x, y, z are not all simultaneously equal to zero, satisfying the system the system of equations

(sin3)x - y + z = 0 ;   (cos2)x + 4y + 3z = 0  and   2x + 7y + 7z = 0

then the number of principal values of  is

a) 2         b) 4         c) 5        d)6

Ques> Number of triplets of a, b and c for which the system of equations,

ax - by = 2a - b    and   (c+1)x + cy = 10 - a + 3b

has infinitely many solutions and x = 1, y = 3 is one of the solutions, is

a) exactly one      b) exactly two      c)exactly three     d) infinitely many