First problem:
x+2y = 10
3x-2y = -2
Just add both equations together to eliminate the "2y". You get:
4x=8, x=2
Now substitute x=2 into the first (or second, doesn't matter) equation, and you get: 2 + 2y = 10, 2y = 8, y=4.
Second problem:
-7x+4y=24
4x-4y=0
Once again, just add both equations together to eliminate the "4y".
-3x = 24, x=-8
Once again, substitute x=-8 into an equation. You get: 8 - 4y = 0, -4y = -8, y=2.
Third problem:
x+y=5
2y-x=-2
Add both equations to eliminate x, and you get: 3y = 3, y=1.
Substitute y=1 into an equation, you get:
x + 1 = 5, x=4.
