I am having trouble understanding system of equations. 
i have tried to work the problem out but im not sure what 
steps to take. can you help me on the problem 

3x/2 +  y/4 = 7
 x/5 - 2y/3 = 2 1/3

We need to clear fractions in each equation:

Put the the 7 of the first equation over 1 so everything 
will be a fraction:

 3x     y     7
---- + --- = ---
  2     4     1

Multiply every term by the LCD of 3 and 4, which is 12.
Put it over 1 too:

 12   3x     12   y     12   7
----·---- + ----·--- = ----·---
  1    2      1   4      1   1

Cancel the 2 into the 12 in the first term, getting 6.  
Cancel the 4 into the 12 in the second term, getting 3.

  6           3 
 12   3x     12   y     12   7
----·---- + ----·--- = ----·---
  1    2      1   4      1   1
       1          1

All that's left is 

            18x + 3y = 84

------------------------

 x/5 - 2y/3 = 2 1/3

Change the 2 1/3 to a mixed fraction 7/3

 x/5 - 2y/3 = 2 1/3


 x     2y     7
--- - ---- = ---
 5      3     3

Multiply every term by the LCD of 5, 3 and 3, which is 15.
Put it over 1 too:
 
 15   x     15   2y     15   7
----·--- - ----·---- = ----·---
  1   5      1    3      1   3
     
Cancel the 5 into the 15 in the first term, getting 3.  
Cancel the 3 into the 15 in the second term, getting 5.
Cancel the 3 into the 15 in the term on the right, 
getting 5

  3          5           5
 15   x     15   2y     15   7
----·--- - ----·---- = ----·---
  1   5      1    3      1   3
      1           1          1

All that's left is 

            3x - 10y = 35 

-----------------------------------------------

Now you have the fractionless system

            18x +  3y = 84
             3x - 10y = 35  

Can you solve that system?  If not post again.

Answer: (x, y) = (5, 2)

Edwin