Find the solution by graph:
4x-20=5y
8x-10y=12

We make a table of values for
each equation:

For 4x - 20 = 5y, we pick
arbitrary values for one
variable and solve for the 
other

  x | y  |   (x, y) 
-----------------------
-10 | -4 | (-10, 4)
 -5 |  0 |  (-5, 0)
  0 |  4 |   (0, 4)
  5 |  8 |   (5, 8)
 10 | 12 | (10, 12)

Plot those 5 points and draw a red line 
through them:



For 8x - 10y = 12, we pick
arbitrary values for one
variable and solve for the 
other

  x | y  |   (x, y)
-------------------
-11 |-10 |(-11, -10)
 -6 | -6 |  (-6, -6)
 -1 | -2 |  (-1, -2)
  4 |  2 |    (4, 2)
  9 |  6 |    (9, 6)
 15 | 16 |  (15, 16)

Plot those 6 points on the same 
set of axes and draw a green line 
through them:

 

Now to find the solution we would
have to find a point where the
red and green lines cross.  However
this is impossible because the two 
lines are parallel and do not cross.
Therefore there is no solution.  We
call such a system "inconsistent".

Edwin