How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #8x -9y = 27# and #9y -8x= -27 #?
The equations are consistent but colinear, so there is no single solution. (see below for method).
For the equation
one obvious solution pair can be obtained by setting
If we want a second pair with integer values, it will take a bit of playing but eventually we might come up with
These two pair of coordinates can be plotted on a Cartesian graph and connected with a straight line as in the first image below.
Similarly, for the equation
we can obtain two pair of coordinates:
Plotting these on a Cartesian graph and connecting with a straight line gives the second graph below.
Combining the two graphs results in overlapping, non-intersecting lines (third graph).
The graph are consistent in as much as they do not contradict each other, but they provide no single solution.