SOLUTION: Solve the system of equations by the method of your choice. Are the equations independent, dependent, or inconsistent? x + y=4 and x-y=5? Thank you Shelley

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the system of equations by the method of your choice. Are the equations independent, dependent, or inconsistent? x + y=4 and x-y=5? Thank you Shelley      Log On


   

Question 330295: Solve the system of equations by the method of your choice. Are the equations independent, dependent, or inconsistent?
x + y=4 and x-y=5?
Thank you
Shelley
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%28x%2By=4%2Cx-y=5%29


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


%28x%2By%29%2B%28x-y%29=%284%29%2B%285%29


%28x%2Bx%29%2B%28y-y%29=4%2B5 Group like terms.


2x%2B0y=9 Combine like terms.


2x=9 Simplify.


x=%289%29%2F%282%29 Divide both sides by 2 to isolate x.


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


x%2By=4 Now go back to the first equation.


9%2F2%2By=4 Plug in x=9%2F2.


2%289%2Fcross%282%29%2By%29=2%284%29 Multiply both sides by the LCD 2 to clear any fractions.


9%2B2y=8 Distribute and multiply.


2y=8-9 Subtract 9 from both sides.


2y=-1 Combine like terms on the right side.


y=%28-1%29%2F%282%29 Divide both sides by 2 to isolate y.


So the solutions are x=9%2F2 and y=-1%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.