Let x be the number of Tables by the Method 1, and

let y be the number of Tables by the Method 2.


Then you have this system of 2 equations in 2 unknowns


    0.5x + 2y = 99        (1)    (hours)    

    9x   + 7y = 564.      (2)    (labor cost)


To solve it,  Multiply equation (1) by 18 (both sides).  Keep equation (2) as is.


    9x +  36y = 99*18     (3)   

    9x   + 7y = 564.      (4)   
    

Subtract equation (4) from equation (3). You will get


    36y - 7y = 99*18 - 564

    29y      = 1218

      y      = 1218/29 = 42.


Substitute the found value of y into equation (1) and find x


     0.5x + 2*42 = 99,

     0.5x = 99 - 2*42 = 15

        x             = 15/0.5 = 30.


ANSWER.  30 tables by Method 1  and  42 tables by Method 2.