SOLUTION: solve by addition, indicate whether each system is independent, dependent or inconsistent. -3x + 3y= -20 2x - 3y = 7

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: solve by addition, indicate whether each system is independent, dependent or inconsistent. -3x + 3y= -20 2x - 3y = 7       Log On


   

Question 395302: solve by addition, indicate whether each system is independent, dependent or inconsistent.
-3x + 3y= -20
2x - 3y = 7
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%28-3x%2B3y=-20%2C2x-3y=7%29


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


%28-3x%2B3y%29%2B%282x-3y%29=%28-20%29%2B%287%29


%28-3x%2B2x%29%2B%283y%2B-3y%29=-20%2B7 Group like terms.


-x%2B0y=-13 Combine like terms.


-x=-13 Simplify.


x=%28-13%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=13 Reduce.


------------------------------------------------------------------


-3x%2B3y=-20 Now go back to the first equation.


-3%2813%29%2B3y=-20 Plug in x=13.


-39%2B3y=-20 Multiply.


3y=-20%2B39 Add 39 to both sides.


3y=19 Combine like terms on the right side.


y=%2819%29%2F%283%29 Divide both sides by 3 to isolate y.


So the solutions are x=13 and y=19%2F3.


Which form the ordered pair .


This means that the system is consistent and independent.


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

Also, feel free to check out my tutoring website

Jim