Solve using the elimination method

7/3x + 5/4y=4
5/6x-2y=21

I am trying to get this concept down for my final, but I have a hard time doing it with fractions for some reason.

If you don't like fractions, you have an equation. Multiply by a common denominator and get rid of them.

Multiply the first equation by 12, for example
12 * (7/3x + 5/4 y) = 4 * 12
12 * 7 / 3 x + 12 * 5 / 4 y = 48
28x + 15 y = 48

Multiply the second equation by 6
6 * (5/6 x - 2y = 21)
30x - 12y = 126

The numbers are bigger, probably more annoying, but at least there aren't any fractions anymore.

I will leave the rest to you.

I would GUESS that question SHOULD read as :-

(7/3)x + (5/4)y = 4
(5/6)x - 2y = 21

28x + 15y = 48
5x - 12y = 126

112 x + 60 y = 192
25x - 60y = 630-----------ADD

137 x = 822
x = 6

30 - 12y = 126
- 96 = 12y
y = - 8

x = 6 , y = - 8