# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 5x-6y=-18 and 6y-5x=18?

Jan 13, 2016

Careful observation reveals that these are the same line.

#### Explanation:

If you take the first equation,

$5 x - 6 y = - 18$

and multiply both sides by -1, you get

$- 5 x + 6 y = 18$

which rearranges to

$6 y - 5 x = 18$

Since they are the same line, ALL solutions for $x$ and $y$ are the same for both lines, so the system is consistent.

The easiest way to graph is to choose two values for $x$, say 0 and 10, and solve for $y$. You can then plot these points $\left(x , y\right)$ and draw a line through both points.

If the lines were NOT the same, you could graph them the same way (choosing values for $x$), and finding the point where the two lines intersect.

To help you visualize what is going on, you may find it useful to play with a graphing calculator such as https://www.desmos.com/calculator.