Question

How do you solve the system of equations `2x-3y=6` and `3y-2x=-6`?

Answer 1

Well, basically you have the same two lines written in a slight diferent form:

You can argue that are two coincident lines with an `oo` number of common points so that your system has `oo` solutions!!!

Answer 2

The easiest method of solving this system will be using elimination. First rewrite the equations where the x terms line up and the y terms line up.

`2x-3y=6`
`-2x+3y=-6`

Now combine (add) the two equations.

`0 = 0`

This means that the lines are actually the same line. They have infinitely many solutions. This is known as a dependent system.