This is how I was taught to do the problem you listed.
Info given: x + 2y = 35 and 3x + 14 y = 120
Step 1: Solve both equations for x.
__x + 2y = 35
____- 2y_____- 2y
__x = 35 - 2y
and
__3x + 14y = 120
_____- 14y______- 14y
__3x = 120 - 14y
_/3____/3____/3
__x = 40 - 14y/3
Now, we know this:
40 - 14y/3 = 35 - 2y
And I'm assuming you can go on from there. The way I learned is probably longer, but it also didn't hurt my brain. 
ETA: Arg! Formatting fail! Added _'s in an attempt to get things to line up. lol
Last edited by epoh; 02/21/12 10:18 AM.
