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

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

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Question 171661: Solve the system of equations using the addition ( elimination) method. If the answer is a unique solution, present it as an oredered pair: ( x,y). If not, specify whether the anser is "no solution or infinitely many solutions." 4x-3y=1
-12x+9y=5
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%284x-3y=1%2C-12x%2B9y=5%29


3%284x-3y%29=3%281%29 Multiply the both sides of the first equation by 3.


12x-9y=3 Distribute and multiply.


So we have the new system of equations:
system%2812x-9y=3%2C-12x%2B9y=5%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:


%2812x-9y%29%2B%28-12x%2B9y%29=%283%29%2B%285%29


%2812x%2B-12x%29%2B%28-9y%2B9y%29=3%2B5 Group like terms.


0x%2B0y=8 Combine like terms. Notice how the x terms cancel out.


0=8Simplify.


Since 0=8 is NEVER true, this means that there are no solutions.


So the system is inconsistent.