SOLUTION: using "solve by elimination" what is the answer to, 7x+2y=10 and negitave 7x+1y= negitave 17

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Question 554702: using "solve by elimination" what is the answer to, 7x+2y=10 and negitave 7x+1y= negitave 17
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%287x%2B2y=10%2C-7x%2By=-17%29


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


%287x%2B2y%29%2B%28-7x%2By%29=%2810%29%2B%28-17%29


%287x%2B-7x%29%2B%282y%2B1y%29=10%2B-17 Group like terms.


0x%2B3y=-7 Combine like terms.


3y=-7 Simplify.


y=%28-7%29%2F%283%29 Divide both sides by 3 to isolate y.


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7x%2B2y=10 Now go back to the first equation.


7x%2B2%28-7%2F3%29=10 Plug in y=-7%2F3.


7x-14%2F3=10 Multiply.


3%287x-14%2Fcross%283%29%29=3%2810%29 Multiply both sides by the LCD 3 to clear any fractions.


21x-14=30 Distribute and multiply.


21x=30%2B14 Add 14 to both sides.


21x=44 Combine like terms on the right side.


x=%2844%29%2F%2821%29 Divide both sides by 21 to isolate x.


So the solutions are x=44%2F21 and y=-7%2F3.


Which form the ordered pair .


This means that the system is consistent and independent.


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Jim