SOLUTION: Hi!! Could you help me solve this linear system using elimination? Please?! x+y=2 2x+7y=9 I tried to solve it myself, and I got (-.5,2.5) i checked the selected answers in the b

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Hi!! Could you help me solve this linear system using elimination? Please?! x+y=2 2x+7y=9 I tried to solve it myself, and I got (-.5,2.5) i checked the selected answers in the b      Log On


   

Question 582763: Hi!! Could you help me solve this linear system using elimination? Please?!
x+y=2
2x+7y=9
I tried to solve it myself, and I got (-.5,2.5) i checked the selected answers in the back of the book and found out the answer is (1,1). Could you help me sove this step by step please?!
THANK YOU!!!!
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=2%2C2x%2B7y=9%29


-2%28x%2By%29=-2%282%29 Multiply the both sides of the first equation by -2.


-2x-2y=-4 Distribute and multiply.


So we have the new system of equations:
system%28-2x-2y=-4%2C2x%2B7y=9%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-2x-2y%29%2B%282x%2B7y%29=%28-4%29%2B%289%29


%28-2x%2B2x%29%2B%28-2y%2B7y%29=-4%2B9 Group like terms.


0x%2B5y=5 Combine like terms.


5y=5 Simplify.


y=%285%29%2F%285%29 Divide both sides by 5 to isolate y.


y=1 Reduce.


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-2x-2y=-4 Now go back to the first equation.


-2x-2%281%29=-4 Plug in y=1.


-2x-2=-4 Multiply.


-2x=-4%2B2 Add 2 to both sides.


-2x=-2 Combine like terms on the right side.


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


x=1 Reduce.


So the solutions are x=1 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 x%2By=2 (red) and 2x%2B7y=9 (green)




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