(1)  If   4x-3y - sqrt(4x-3y) = 56,  then introduce  t = sqrt(4x-3y) and get the equation


         t^2 - t = 56,  t^2 - t - 56 = 0,  (t-8)*(t+7) = 0.

     
     The roots are 8 or -7.  In what follows, I will consider only positive value of .


     So,  sqrt(4x-3y) = 8;  hence,  4x - 3y = 64.




(2)  Follow by the same way, and from the second equation,  7x-2y + sqrt(7x-2y) = 12  find


         t = sqrt(7x-2y),  t^2 +t -12 = 0,  (t-3)*(t+4) = 0.


     Of the two roots for sqrt, take only positive  t= 3.


     It gives  sqrt(7x-2y) = 3;  hence  7x - 2y = 9.




(3)  Now you have the system of 2 equations in 2 unknowns


         4x - 3y = 64,

         7x - 2y =  9.


     Solve it by any way and any method you know (it is just arithmetic) and find x and y.



(4)  Then calculate x-y.