SOLUTION: 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 answe

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 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 answe      Log On


   

Question 174563: 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.”
4x – 3y = 1
-12x + 9y = 5
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%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.


0=8Simplify.


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