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

Apr 25, 2016

They have infinitely many solutions.

Explanation:

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

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.