# 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 ?

Jan 16, 2016

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

#### Explanation:

For the equation $\textcolor{red}{8 x - 9 y = 27}$
one obvious solution pair can be obtained by setting $x = 0$ giving $\left(\textcolor{red}{0 , - 3}\right)$
If we want a second pair with integer values, it will take a bit of playing but eventually we might come up with $\left(\textcolor{red}{9 , 5}\right)$
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 $\textcolor{b l u e}{9 y - 8 x = - 27}$
we can obtain two pair of coordinates: $\left(\textcolor{b l u e}{0 , - 3}\right)$ and $\left(\textcolor{b l u e}{9 , 5}\right)$.
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. 