Question 69844
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To find y we eliminate x:

To eliminate the x terms, look at the coefficients
of x:

2x – 4y = 7
4x + 2y = 9

They are 2 and 4.   Their least common multiple in
absolute value is 4. Multiply the first equation 
through by -2 to make the 2x become -4x, so it will 
cancel with the 4x in the second equation:

-2[2x - 4y = 7]
   4x + 2y = 9 

  -4x + 8y = -14
   4x + 2y =   9

Now add vertically term-by-term:

  -4x + 8y = -14
  <u> 4x + 2y =   9</u>
       10y =  -5
         y = -5/10
         y = -1/2


To find x we eliminate y:

To eliminate the y terms, look at the coefficients
of y:

2x – 4y = 7
4x + 2y = 9

They are -4 and 2.   Their least common multiple in
absolute value is 4. Multiply the second equation 
through by 2 to make the 2y become 4y, so it will 
cancel with the -4y in the first equation:

   2x - 4y = 7
 2[4x + 2y = 9] 

   2x - 4y =  7
   8x + 4y = 18

Now add vertically term-by-term:

   2x - 4y =  7
  <u> 8x + 4y = 18</u>
  10x      = 25
         x = 25/10
         x = 5/2

So the solution is (x,y) = (5/2,-1/2) 

Edwin</pre>