1.  One way to solve it is using determinant.


2.  The other way is  THIS:

    the system has INFINITELY MANY solutions if and only if the two equations are equivalent.

    In other words, if and only if

     =  = .    (1)

    (the coefficients and the right side terms are proportional with the same proportionality coefficient).


3.   From   =   you have   = 9  ====>  k+1 = +/-3  ====>  a) k = -1 + 3 = 2,  and  b) k = -1 - 3 = -4.



     Now check k = 2 for this proportion:  = .

     You have  =  (left side)  and   =  =   (right side).

     So, the value k = 2 satisfies (1).



     Now check k = -4 for this proportion:  = .

     You have  =  (left side)  and   =   (right side).

     So, the value k = -4 does not satisfy (1).