Question 417563
4y=2x-10
4y=2(5+2y)-10
4y=10+4y-10
4y-4y=10-10
0=0
------------
I get what what the teacher has in mind. At the beginning, there
must have been 2 equations:

(1)   {{{4y = 2x - 10}}}
and
(2)   {{{x = 5 + 2y}}}

What the teacher was trying to show is that these equations are
exactly the same. (S)he did this by trying to "solve" for x and y
in the normal way, by substitution. If the equations were different,
this would have resulted in a solution (x,y).
-------------
To show the equations are the same, subtract {{{5}}} from both sides
of (2). Then you have:
 (2)       {{{2y = x - 5}}}
Now multiply both sides by {{{2}}}
(2)        {{{4y = 2x - 10}}}
So, if both equations are the same, there is no solution. Also if the 
equations are different, but have the same slope, tyhere can be no
solution, since they would be parallel lines that never meet.
An example would be:

(1)  {{{y = 7x - 4}}}
(2)  {{{y = 7x + 11}}}