SOLUTION: 3x-2y=2 -2x+y=-2 So the answer is (-2,-6) right? And how do you know when consistent,dependent,inconsistent,or dependent? >Thats my main issue. Thanks

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 3x-2y=2 -2x+y=-2 So the answer is (-2,-6) right? And how do you know when consistent,dependent,inconsistent,or dependent? >Thats my main issue. Thanks      Log On


   

Question 367272: 3x-2y=2
-2x+y=-2
So the answer is (-2,-6) right? And how do you know when consistent,dependent,inconsistent,or dependent? >Thats my main issue.
Thanks
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-2y=2%2C-2x%2By=-2%29


2%28-2x%2By%29=2%28-2%29 Multiply the both sides of the second equation by 2.


-4x%2B2y=-4 Distribute and multiply.


So we have the new system of equations:
system%283x-2y=2%2C-4x%2B2y=-4%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:


%283x-2y%29%2B%28-4x%2B2y%29=%282%29%2B%28-4%29


%283x%2B-4x%29%2B%28-2y%2B2y%29=2%2B-4 Group like terms.


-x%2B0y=-2 Combine like terms.


-x=-2 Simplify.


x=%28-2%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=2 Reduce.


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3x-2y=2 Now go back to the first equation.


3%282%29-2y=2 Plug in x=2.


6-2y=2 Multiply.


-2y=2-6 Subtract 6 from both sides.


-2y=-4 Combine like terms on the right side.


y=%28-4%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=2 Reduce.


So the solutions are x=2 and y=2.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 3x-2y=2 (red) and -2x%2By=-2 (green)

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Notes: If the system has one unique solution, then the system is both independent and consistent.


If the system has no solutions, then the system is inconsistent.


If the system has an infinite number of solutions, then the system is consistent and dependent.



If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim