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
Alan P.
Jan 16, 2016

The equations are consistent but colinear, so there is no single solution. (see below for method).

Explanation:

For the equation #color(red)(8x-9y=27)#
one obvious solution pair can be obtained by setting #x=0# giving #(color(red)(0,-3))#
If we want a second pair with integer values, it will take a bit of playing but eventually we might come up with #(color(red)(9,5))#
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 #color(blue)(9y-8x=-27)#
we can obtain two pair of coordinates: #(color(blue)(0,-3))# and #(color(blue)(9,5))#.
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.
enter image source here

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