Question 69431
Let's start with #1:

x + y = 6
    y = 2x.
</br></br>
There are a few ways to solve these, but the substitution method is often easiest.  
</br></br>
1.  Substitute 2x in for y in the 1st equation:     x + (2x) = 6.
(This can be done because the 2nd equation says y and 2x are interchangeable).
</br></br>
2.  Simplify:                                        3x = 6.
</br></br>
3.  Solve for x:                                      x = 2.
</br></br>
4.  Plug 2 in for x in the 1st equation:              2 + y = 6.
</br></br>
5.  Solve for y:                                        y = 4.
</br></br>
6.  Final Answer:                                      (2, 4).  (x = 2, y = 4).
</br></br>

That's the substitution method - the next example has a few more steps:
</br></br>
2x-3y=-13
   y=2x+7 
</br></br>
1.  Substitute 2x + 7 in for y in the 1st equation:     2x - 3(2x + 7) = -13.
(This can be done because the 2nd equation says y and 2x + 7 are interchangeable).
</br></br>
2.  Simplify:                                        -4x - 21 = -13.
</br></br>
3.  Solve for x:                                      x = -2.
</br></br>
4.  Plug -2 in for x in the 1st equation:              2(-2) - 3y = -13.
</br></br>
5.  Solve for y:                                        y = 3.
</br></br>
6.  Final Answer:                                      (-2, 3). (x = -2, y = 3).