SOLUTION: Solve each system by the addition method. x/3 - y/2 = -5/6 x/5 - y/3 = -3/5

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Question 79234: Solve each system by the addition method.
x/3 - y/2 = -5/6
x/5 - y/3 = -3/5
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!


Solve each system by the addition method.

x/3 - y/2 = -5/6
x/5 - y/3 = -3/5

%28x%2F3%29+-+%28y%2F2%29+=+-5%2F6
%28x%2F5%29+-+%28y%2F3%29+=+-3%2F5

You should clear of fractions first.

Clear the first of fractions by multiplying 
through by 6%2F1: 

%286%2F1%29%28x%2F3%29+-+%286%2F1%29%28y%2F2%29+=+%286%2F1%29%28-5%2F6%29

   2x - 3y = -5

Clear the second of fractions by multiplying 
through by 15%2F1: 

x/5 - y/3 = -3/5

%2815%2F1%29%28x%2F5%29+-+%2815%2F1%29%28y%2F3%29+=+%2815%2F1%29%28-3%2F5%29

   3x - 5y = -9

So we have the system

   2x - 3y = -5
   3x - 5y = -9

The coefficients of y are -3 and -5. The LCM of
their absolute values is 15, so 

1. We need to make the -3 in the first into a -15 
by multiplyng the whole first equation through by 5.
2. We need to make the -5 in the second into a +15 
by multiplyng the whole second equation through by -3.

 (5)2x -  (5)3y =  (5)(-5)
(-3)3x - (-3)5y = (-3)(-9)

which when simplified becomes:

     10x - 15y = -25
     -9x + 15y =  27

Add term by term vertically

    10x - 15y = -25
    -9x + 15y =  27
   ------------------
      x       =   2


Substitute 2 for x in

   2x - 3y = -5

 2(2) - 3y = -5
    4 - 3y = -5
       -3y = -5 - 4
       -3y = -9
          y = (-9)/(-3)
          y = 3

So the solution is (x,y) = (2,3).

Edwin