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 = 

3x + 4y - 2xy = 4

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


Multiply through by 

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 =              y = 


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 = 

Substitute in 

x = 

x = 

x =  =  = 1

So one solution is (x,y) = (1,)

Find the x-value that corresponds to y = 

Substitute in 

x = 

x = 

x =  =  

Multiply top and bottom by 3

x =  =  =  = 


So the other solution solution is (x,y) = (,)

Edwin