SOLUTION: plaase help me solve this system equations x+2y+2xy=3 and 3x+4y-2xy=4

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Question 468875: plaase help me solve this system equations x+2y+2xy=3 and 3x+4y-2xy=4
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
 x + 2y + 2xy = 3
3x + 4y - 2xy = 4

Solve the first one for x

 x + 2y + 2xy = 3
      x + 2xy = 3 - 2y
    x(1 + 2y) = 3 - 2y
            x = %283-2y%29%2F%281%2B2y%29

3x + 4y - 2xy = 4

3(%283-2y%29%2F%281%2B2y%29) + 4y - 2(%283-2y%29%2F%281%2B2y%29)y = 4


Multiply through by %281%2B2y%29

3(3 - 2y) + 4y(1 + 2y) - 2(3 - 2y)y = 4(1 + 2y)

3(3 - 2y) + 4y(1 + 2y) - 2y(3 - 2y) = 4(1 + 2y)


       9 - 6y + 4y + 8y² - 6y + 4y² = 4 + 8y

                      9 - 8y + 12y² = 4 + 8y

Get 0 on the right side:

                     12y² - 16y + 5 = 0  
Factor:
                   (2y - 1)(6y - 5) = 0

Use zero-factor property:

          2y - 1 = 0         6y - 5 = 0

              2y = 1             6y = 5
             
               y = 1%2F2             y = 5%2F6


So there are going to be two solutions.  We must find
the x-value that corresponds to each one.

Find the x-value that corresponds to y = 1%2F2

Substitute in 

x = %283-2y%29%2F%281%2B2y%29

x = %283-2%281%2F2%29%29%2F%281%2B2%281%2F2%29%29

x = %283-1%29%2F%281%2B1%29 = 2%2F2 = 1

So one solution is (x,y) = (1,1%2F2)

Find the x-value that corresponds to y = 5%2F6

Substitute in 

x = %283-2y%29%2F%281%2B2y%29

x = %283-2%285%2F6%29%29%2F%281%2B2%285%2F6%29%29

x = %283-10%2F6%29%2F%281%2B10%2F6%29 = %283-5%2F3%29%2F%281%2B5%2F3%29 

Multiply top and bottom by 3

x = %283%283-5%2F3%29%29%2F%283%281%2B5%2F3%29%29 = %289-5%29%2F%283%2B5%29 = 4%2F8 = 1%2F2


So the other solution solution is (x,y) = (1%2F2,5%2F6)

Edwin