It's called the substitution method.
EG
We have the sim equations
and
Then we solve for a variable in one of the equations and substitute for the variable in the other
Now we sub for y in the other
solve for x and we can determine the solution
Now we put back in the original for x.
Do you see?
Think of it like a game, with the object being to line thx's and y's up underneath of each other and then add or subtract them to get rid of one of them.
You can see here that the x's and y's are not right underneath of each other, but wait...
Now the x's and y's are lined up. But remember that the object is to add (or subtract) so that I eliminate one of the variables. To do this I have to do a little trick with multiplication...
Now look! The x's and y's are still lined up, but now if I subtract the two equations, the x's will dissapear and I can solve for y!
Do you see?