SOLUTION: Solve each system by the addition method: 3/7x+5/9y=27 1/9x+2/7y=7

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Question 147009: Solve each system by the addition method:
3/7x+5/9y=27
1/9x+2/7y=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%283%2F7%29x%2B%285%2F9%29y=27 Start with the first equation.


63%28%283%2Fcross%287%29%29x%2B%285%2Fcross%289%29%29y%29=63%2827%29 Multiply both sides by the LCD 63 to clear any fractions.


27x%2B35y=1701 Distribute and multiply.



%281%2F9%29x%2B%282%2F7%29y=7 Now move onto the next equation.


63%28%281%2Fcross%289%29%29x%2B%282%2Fcross%287%29%29y%29=63%287%29 Multiply both sides by the LCD 63 to clear any fractions.


7x%2B18y=441 Distribute and multiply.




Start with the given system of equations:
system%2827x%2B35y=1701%2C7x%2B18y=441%29


-7%2827x%2B35y%29=-7%281701%29 Multiply the both sides of the first equation by -7.


-189x-245y=-11907 Distribute and multiply.


27%287x%2B18y%29=27%28441%29 Multiply the both sides of the second equation by 27.


189x%2B486y=11907 Distribute and multiply.


So we have the new system of equations:
system%28-189x-245y=-11907%2C189x%2B486y=11907%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:


%28-189x-245y%29%2B%28189x%2B486y%29=%28-11907%29%2B%2811907%29


%28-189x%2B189x%29%2B%28-245y%2B486y%29=-11907%2B11907 Group like terms.


0x%2B241y=0 Combine like terms. Notice how the x terms cancel out.


241y=0 Simplify.


y=%280%29%2F%28241%29 Divide both sides by 241 to isolate y.


y=0 Reduce.


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-189x-245y=-11907 Now go back to the first equation.


-189x-245%280%29=-11907 Plug in y=0.


-189x%2B0=-11907 Multiply.


-189x=-11907 Remove any zero terms.


x=%28-11907%29%2F%28-189%29 Divide both sides by -189 to isolate x.


x=63 Reduce.


So our answer is x=63 and y=0.


Which form the ordered pair .


This means that the two equations are consistent and independent.