Question 145138
This site has a good explanation of the "elimination method":
http://www.purplemath.com/modules/systlin6.htm

1)5x - y = 12
  3x + y = 4
  ------------ start by adding both equations together to get rid of the 'y'
  8x = 16
   x = 2 (dividing both sides by 8)
To find y, substitute x back into either of the two equations:
5x - y = 12
5(2) - y = 12
10 - y = 12
-y = 2
y = -2

2)2x - y = -6
  2x - 2y = -4
 
multiply the second equation by -1 to get:
2)2x - y = -6
 -2x + 2y = 4
-------------  add both equations together
      y = -2
To find x, substitute y back into either of the two equations:
2x - y = -6
2x - (-2) = -6
2x + 2 = -6
2x = -8
x = -4