SOLUTION: How can you solve the following system of euqations for x? 2x+y=7 x-y=2

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Question 196630: How can you solve the following system of euqations for x?
2x+y=7
x-y=2
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=7%2Cx-y=2%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-y%29=%287%29%2B%282%29


%282x%2Bx%29%2B%28y-y%29=7%2B2 Group like terms.


3x%2B0y=9 Combine like terms. Notice how the "y" terms cancel out.


3x=9 Simplify.


x=%289%29%2F%283%29 Divide both sides by 3 to isolate x.


x=3 Reduce.


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


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


2%283%29%2By=7 Plug in x=3.


6%2By=7 Multiply.


y=7-6 Subtract 6 from both sides.


y=1 Combine like terms on the right side.


So the solutions are x=3 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=7 (red) and x-y=2 (green)