SOLUTION: i need step by step solution using elimination method x-2y-8 x+2y-0

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Question 148095This question is from textbook
: i need step by step solution using elimination method
x-2y-8
x+2y-0 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the system is: system%28x-2y=8%2Cx%2B2y=0%29


Start with the given system of equations:
system%28x-2y=8%2Cx%2B2y=0%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-2y%29%2B%28x%2B2y%29=%288%29%2B%280%29


%28x%2Bx%29%2B%28-2y%2B2y%29=8%2B0 Group like terms.


2x%2B0y=8 Combine like terms. Notice how the y terms cancel out.


2x=8 Simplify.


x=%288%29%2F%282%29 Divide both sides by 2 to isolate x.


x=4 Reduce.


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x-2y=8 Now go back to the first equation.


4-2y=8 Plug in x=4.


4-2y=8 Multiply.


-2y=8-4 Subtract 4 from both sides.


-2y=4 Combine like terms on the right side.


y=%284%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=-2 Reduce.


So our answer is x=4 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-2y=8 (red) and x%2B2y=0 (green)