SOLUTION: 2x-y=-3 x+y=9

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Question 395473: 2x-y=-3
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%282x-y=-3%2Cx%2By=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:


%282x-y%29%2B%28x%2By%29=%28-3%29%2B%289%29


%282x%2Bx%29%2B%28-y%2By%29=-3%2B9 Group like terms.


3x%2B0y=6 Combine like terms.


3x=6 Simplify.


x=%286%29%2F%283%29 Divide both sides by 3 to isolate x.


x=2 Reduce.


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


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


4-y=-3 Multiply.


-y=-3-4 Subtract 4 from both sides.


-y=-7 Combine like terms on the right side.


y=%28-7%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=7 Reduce.


So the solutions are x=2 and y=7.


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 2x-y=-3 (red) and x%2By=9 (green)


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

Also, feel free to check out my tutoring website

Jim