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
