Question

How do you tell whether the system `9x-9y=27` and `9y-9x= -27`has no solution or infinitely many solutions?

Answer 1

They have infinitely many solutions.

Explanation:

The two equations are `9x-9y=27` and `9y-9x=-27`.

In fact second equation can be derived from first by multiplying it by `-1`. They both lead to `x=y+3`.

Hence essentially the equations are same. In other words the lines have all the points satisfying both the equations, wherever `x=y+3`. In other words,

They have infinitely many solutions.