If everything cancels out then it means you really only have one equation because -9x-3y=-18 and 3x+y=6 are the same thing.
3x + y = 6
multiply both sides by -3
-9x -3y = -18
same thing
That means there is not a unique solution (only one possible value for x and for y). That means there are an infinite number of solutions.
You can pick any value for x and get a y value that works:
x = 437 (example)
3*437 + y = 6
1311 + y = 6
y = -1305
Answer: x = 437, y = -1305
You can pick any value for y and get an x value that works:
y = 36 (example)
3x + y = 6
3x + 36 = 6
3x = -30
x = -10
Answer: x = -10, y = 36