SOLUTION: -x+6y=3 3x-2y=5

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Question 201105: -x+6y=3
3x-2y=5
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%28-x%2B6y=3%2C3x-2y=5%29


3%28-x%2B6y%29=3%283%29 Multiply the both sides of the first equation by 3.


-3x%2B18y=9 Distribute and multiply.


So we have the new system of equations:
system%28-3x%2B18y=9%2C3x-2y=5%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:


%28-3x%2B18y%29%2B%283x-2y%29=%289%29%2B%285%29


%28-3x%2B3x%29%2B%2818y-2y%29=9%2B5 Group like terms.


0x%2B16y=14 Combine like terms.


16y=14 Simplify.


y=%2814%29%2F%2816%29 Divide both sides by 16 to isolate y.


y=7%2F8 Reduce.


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-3x%2B18y=9 Now go back to the first equation.


-3x%2B18%287%2F8%29=9 Plug in y=7%2F8.


-3x%2B63%2F4=9 Multiply.


4%28-3x%2B63%2Fcross%284%29%29=4%289%29 Multiply both sides by the LCD 4 to clear any fractions.


-12x%2B63=36 Distribute and multiply.


-12x=36-63 Subtract 63 from both sides.


-12x=-27 Combine like terms on the right side.


x=%28-27%29%2F%28-12%29 Divide both sides by -12 to isolate x.


x=9%2F4 Reduce.


So the solutions are x=9%2F4 and y=7%2F8.


Which form the ordered pair .


This means that the system is consistent and independent.