Question

Use the elimination method to solve the system.
x-3y=9
-x+3y=-9

Answer 1

Let's eliminate x:
x = 9+3y (from the first equation)
Second equation now becomes:
-(9+3y)+3y=-9
-9-3y+3y=-9
-9=-9

True for all values of y.

Answer 2

y=-9

Answer 3

No, y is any real number.

Answer 4

1st : (some number)-3(some other number)=9
(some number) =[9+3(some other number)]
2nd: we have a better definition of (some number), here being the letter X,
so we continue refining the second equation using the first one
(given the fact both equations are true and relate to one another)

-(some number)+3(some other number)=-9

we replace the data for x (some number) with the refined definition:

-[9+3(some other number)]+3(some other number)=-9
-9-3(some other number)+3(some other number) = -9
the -3(some other number) and the +3(some other number) cancel out, giving

-9 = -9

I stress on the fact that (some number) represents x and (some other number) represents y, these symbols can be anything. As long as the valua of X is the same in both equations, as goes for the value of Y, these equations will be true to one another.

Sorry for the dumbed-down version, but many students have issues with even the simplest concepts in mathematics, expecially the use of symbols to represent any given number or value