SOLUTION: x+y=7 x-y=3

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Question 567964: x+y=7
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%28x%2By=7%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:


%28x%2By%29%2B%28x-1y%29=%287%29%2B%283%29


%281x%2B1x%29%2B%281y%2B-1y%29=7%2B3 Group like terms.


2x%2B0y=10 Combine like terms.


2x=10 Simplify.


x=%2810%29%2F%282%29 Divide both sides by 2 to isolate x.


x=5 Reduce.


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x%2By=7 Now go back to the first equation.


5%2By=7 Plug in x=5.


y=7-5 Subtract 5 from both sides.


y=2 Combine like terms on the right side.


So the solutions are x=5 and y=2.


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 x%2By=7 (red) and x-y=3 (green)