Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `6x - 9y = 18` and `9y - 6x = -18`?

Answer 1

I would say Consistent.

Explanation:

Let us write our equations as:

`color(red)(6x-9y=18)`

that can be written as:
`y=2/3x-2`
and:

`color(red)(-6x+9y=-18)`

that, again, can be written as:
`y=2/3x-2`

you can see that the second equation is the first multiplied by `-1` so the two equations represent two straight lines one superimposed over the other (coincident lines) so they will have infinite points in common and our system will have infinite solutions and so will be a consistent system.

We can plot them as two coincident lines of equation `y=2/3x-2`:
graph{2/3x-2 [-10, 10, -5, 5]}