# 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.