SOLUTION: Solve the system of equations x + y = 6 x - y = -9

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Question 530986: Solve the system of equations
x + y = 6
x - y = -9
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=6%2Cx-y=-9%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-1y%29=%286%29%2B%28-9%29


%281x%2B1x%29%2B%281y%2B-1y%29=6%2B-9 Group like terms.


2x%2B0y=-3 Combine like terms.


2x=-3 Simplify.


x=%28-3%29%2F%282%29 Divide both sides by 2 to isolate x.


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


x%2By=6 Now go back to the first equation.


-3%2F2%2By=6 Plug in x=-3%2F2.


2%28-3%2Fcross%282%29%2By%29=2%286%29 Multiply both sides by the LCD 2 to clear any fractions.


-3%2B2y=12 Distribute and multiply.


2y=12%2B3 Add 3 to both sides.


2y=15 Combine like terms on the right side.


y=%2815%29%2F%282%29 Divide both sides by 2 to isolate y.


So the solutions are x=-3%2F2 and y=15%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.


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Jim