For example, you have:
ax + by = c
dx + ey = f
You start off by rearranging one of the two:
ey = f - dx
y = (f/e) - (d/e)x
The you substitute it into the other equation:
ax + b[(f/e) - (d/e)x] = c
After simplfying, you will get x equal something.
Substitute that into y = (f/e) - (d/e)x to get the value of y.
With that, you are done.