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

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Question 557487: 2x+y=3
x-y=3
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%2By=3%2Cx-y=3%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%2By%29%2B%28x-1y%29=%283%29%2B%283%29


%282x%2B1x%29%2B%281y%2B-1y%29=3%2B3 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%2By=3 Now go back to the first equation.


2%282%29%2By=3 Plug in x=2.


4%2By=3 Multiply.


y=3-4 Subtract 4 from both sides.


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


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


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

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Jim