SOLUTION: All 30 students in a class study at least one of the two subjects History and Geography. Twice as many study History as Geography. 8 students study only Geography. By drawing a V

Let x students study only History; 

    y students study only Geography;

    z students study both subjects.


Then we have these three equations

     x + y + z = 30      (1)

     x + z = 2*(y+z)     (2)

     y = 8               (3)


Substutitute y= 8 from equation (3) into equations (1) and (2)

    x + 8 + z = 30       (1')

    x + z = 2*(8+z)      (2')


Simplify

    x + z = 22           (1'')

    x - z = 16           (2'')


From equations (1'')  and (2'') you get by adding       2x = 22+16 = 38,  x = 38/2 = 19.

From equations (1'')  and (2'') you get by subtracting  2z = 22-16 =  6,  z = 6/2 = 3.


Thus 19 students study only History;  8 students study only Geography, and 3 students study both subjects.


ANSWER.  3 students study both subjects.