SOLUTION: Solve the system of equations using the addution (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x,y). If not, specify whether the answe

Algebra ->  Linear-equations -> SOLUTION: Solve the system of equations using the addution (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x,y). If not, specify whether the answe      Log On


   

Question 180713: Solve the system of equations using the addution (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 by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x-11y=9%2C-9x%2B33y=-27%29


3%283x-11y%29=3%289%29 Multiply the both sides of the first equation by 3.


9x-33y=27 Distribute and multiply.


So we have the new system of equations:
system%289x-33y=27%2C-9x%2B33y=-27%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%289x-33y%29%2B%28-9x%2B33y%29=%2827%29%2B%28-27%29


%289x%2B-9x%29%2B%28-33y%2B33y%29=27%2B-27 Group like terms.


0x%2B0y=0 Combine like terms.


0=0Simplify.


Since 0=0 is always true, this means that there are an infinite number of solutions.


So the system is consistent and dependent.