Question

Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions" and state how you arrived at that conclusion.
3x - 11y = 9
-9x + 33y = -27

Answer 1

Did you notice that if you multiply the first equation by -3 you get the second equation?
or, as I guess happened when you did this question,
if you multiply the first equation by 3 and then add the two equations you end up with 0 = 0

If that happens there will be an infinite number of solutions.
(you are really only dealing with one equations whose graph is a straight line, and a straight line has an infinite number of points on it)

However, had your first equation been
3x - 11y = 8
then multiplying it by 3 and then adding it to the second equation would give you
0 = -3 which of course is FALSE.
then there would be no solution.

(your graph would be two parallel lines which would never meet, thus no solution)

Answer 2

thank you