Question

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`?

Answer 1

Careful observation reveals that these are the same line.

Explanation:

If you take the first equation,

`5x-6y=-18`

and multiply both sides by -1, you get

`-5x+6y=18`

which rearranges to

`6y-5x=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 `(x,y)` 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.