(okay well someone else wrote an answer as well but i was writing mine and i don't want my work to go to waste so i'll just post it okay)
3x-4y=4
9x-7y=22
Well, the first thing you need to keep in mind is that, based on what is easiest, either the x's or y's should be comprised of the same number, except on negative and one positive. (or both the same if you'll subtract the equations instead)
In this case, it'd be easier to just multiply the first equation by -3. Saves time and smaller numbers.
So:
-9x+12y=-12
9x-7y=22
So, heres the thing, we add up the equations. (Why? Because logically speaking, if -9x+12y=-12 and 9x-7y=22, then -9x+9x+12y-7y=-12+22 )
So basically: (see spoiler)
I added -9x+(+9x) to give 0. This was why we multiplied, so that we could eliminate one of the variables.
Then +12y+(-7y) to give +5y. Then, then last one is explanatory.
Now that you know y, substitute it in any of the original equations and get x.
Then test both x and y in the remaining equation to make sure it gives the same end result.
(p.s I know I did a slightly more complicated route, but that's what I was used to. I can't believe I never thought of the subtract method before. That's my whole life lived like this. What a life it was)