How do you solve this weird system of equations?

Question

6/x-7/y= 8
15/x-14/y=21

Answer 1

sub 1/x = u and 1/y = w

then 6u - 7w = 8
and 15u - 14w = 21

12u - 14w = 16
15u - 14w = 21
3u = 5 u = 5/3
10 - 7w = 8
-7w = -2, w = 2/7

so x = 3/5 and y = 7/2

Answer 2

First, you take one of the equations-the easiest to do this with is the first one-and solve for only one variable.

6/x-7/y=8, multiply by xy
6y-7x=8xy
6y=8xy+7x, divide by 6
y=8xy/6 +7x/6

You now have the equation for one variable. Substitute it for y in the second equation and you will find out what x is. Then take that, substitute in the first equation, and you will know what x and y are. Good luck.