SOLUTION: 8x-4y=12 2x-8y=3

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Question 324151: 8x-4y=12 2x-8y=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%288x-4y=12%2C2x-8y=3%29


-2%288x-4y%29=-2%2812%29 Multiply the both sides of the first equation by -2.


-16x%2B8y=-24 Distribute and multiply.


So we have the new system of equations:
system%28-16x%2B8y=-24%2C2x-8y=3%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:


%28-16x%2B8y%29%2B%282x-8y%29=%28-24%29%2B%283%29


%28-16x%2B2x%29%2B%288y%2B-8y%29=-24%2B3 Group like terms.


-14x%2B0y=-21 Combine like terms.


-14x=-21 Simplify.


x=%28-21%29%2F%28-14%29 Divide both sides by -14 to isolate x.


x=3%2F2 Reduce.


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-16x%2B8y=-24 Now go back to the first equation.


-16%283%2F2%29%2B8y=-24 Plug in x=3%2F2.


-24%2B8y=-24 Multiply.


8y=-24%2B24 Add 24 to both sides.


8y=0 Combine like terms on the right side.


y=%280%29%2F%288%29 Divide both sides by 8 to isolate y.


y=0 Reduce.


So the solutions are x=3%2F2 and y=0.


Which form the ordered pair .


This means that the system is consistent and independent.