Question

x - 3y =-2

-3x +9y =2

Answer 1

Multiply the 1st equation by -3 and you have
-3x+9y = 6
-3x+9y = 6

So, both equations describe the same line. Any solution to one is also a solution of the other.

Answer 2

You are trying to solve two equations which are represented
by two parallel lines. There will be no solution, since parallel
lines will never intersect.

Here is what will happen:
multiply the first by 3, then add them
3x - 9y = 6
-3x + 9y = 2
0 = 2
this is a false statement.

If in solving 2 equations of this type, the variables drop out ....
1. you end up with a false statement, like ours above, there will
be no solution.
2. you end up with a true statement, then the two equations are
really just the same line, and there will be an infinite number of
solutions.

Answer 3

Looks like both Steve and me both made silly
arithmetic errors.
My answer to the addition should have been
0 = 8 , but the conclusion and what follows is still valid.

Answer 4

You mean 2 ≠ 9 ?
Dang!