Posted by **Gail** on Tuesday, March 24, 2009 at 7:23pm.

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

- Math -
**Reiny**, Tuesday, March 24, 2009 at 7:41pm
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)

- Math -
**Gail**, Tuesday, March 24, 2009 at 8:09pm
thank you

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