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 #?
1 Answer
The equations are consistent but colinear, so there is no single solution. (see below for method).
Explanation:
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.