SOLUTION: solve using any methord x/3-y/2=3 x/2+y/3=7/3

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Question 168735: solve using any methord
x/3-y/2=3
x/2+y/3=7/3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%2F3-y%2F2=3 Start with the first equation.


6%28x%2Fcross%283%29%29-6%28y%2Fcross%282%29%29=6%283%29 Multiply EVERY term by the LCD 6 to clear the fractions.


2x-3y=18 Multiply and simplify


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x%2F2%2By%2F3=7%2F3 Move onto the second equation.


6%28x%2Fcross%282%29%29%2B6%28y%2Fcross%283%29%29=6%287%2Fcross%283%29%29 Multiply EVERY term by the LCD 6 to clear the fractions.


3x%2B2y=14 Multiply and simplify


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So we have the system of equations:

system%282x-3y=18%2C3x%2B2y=14%29


2%282x-3y%29=2%2818%29 Multiply the both sides of the first equation by 2.


4x-6y=36 Distribute and multiply.


3%283x%2B2y%29=3%2814%29 Multiply the both sides of the second equation by 3.


9x%2B6y=42 Distribute and multiply.


So we have the new system of equations:
system%284x-6y=36%2C9x%2B6y=42%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:


%284x-6y%29%2B%289x%2B6y%29=%2836%29%2B%2842%29


%284x%2B9x%29%2B%28-6y%2B6y%29=36%2B42 Group like terms.


13x%2B0y=78 Combine like terms. Notice how the y terms cancel out.


13x=78 Simplify.


x=%2878%29%2F%2813%29 Divide both sides by 13 to isolate x.


x=6 Reduce.


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4x-6y=36 Now go back to the first equation.


4%286%29-6y=36 Plug in x=6.


24-6y=36 Multiply.


-6y=36-24 Subtract 24 from both sides.


-6y=12 Combine like terms on the right side.


y=%2812%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=-2 Reduce.


So our answer is x=6 and y=-2.


Which form the ordered pair .