6x+3y=6xy and 2x+4y=5xy(cross multiplication)

6x+ 3y =6xy  --------  (1)  ,     2x +4y = 5 xy  ------   (2)

divide each term of both equations by   (xy)

  6 x / xy + 3y / xy = 6 xy /xy   is  6 /y + 3 /x  - 6 = 0 . Let 1 /x  = a and  1 / y = b

such that 3a + 6 b  -- 6 = 0  ----------   (3)

eqn. (2) becomes  4a + 2b -- 5  = 0  ---------   (4)

solving eqns. 3 and 4 by cross multiplication

             a                  b               1

--------------  =  ------------  =  ----------

- 30 + 12          -24 +15         6 - 24

      a / - 18  =  b / -9   =1  / -18

a = -18/ -18  = 1  ,      b  = -9 / -18  =1 /2

now a = 1 /x = 1  ,   x = 1

      b = 1/y = 1/2       y = 2