SOLUTION: linear algebra elimination method 13) 2/3x+2/5y=4/5 1/2x+2/3y=-1/2 12)9/14x+y=19/7 -20x+21y=144 11)x+5/3y=7/3 2/5x-y=3/5 10)x+9/4y=7/4 5/9x-y=2/9 8)18x

I'll just do this one: 

 x + y = 
 -20x + 21y = 144

To clear the first one of fractions multiply 
every term by the LCD of 14:

14·x + 14·y = 14·
  
9x + 14y = 38

Now we have the system:

  9x + 14y =  38
-20x + 21y = 144

The idea is to eliminate a variable:
The coefficients of y are 14 and 21
The least common multiple of 14 and 21
is 42.  To make the coefficients of
y equal in absolute value yet opposite
in sign we multiply the first equation
through by -3 and the second equation
through by 2.  That will make the
coefficients -42 and +42:

-3[  9x + 14y] = -3[38]
 2[-20x + 21y] =  2[144]

   -27x - 42y = -114
   -40x + 42y =  288

Now we add those term by term:

   -27x - 42y = -114
   -40x + 42y =  288
  -------------------
   -67x       =  174
      x       =  

Since that is too complicated a fraction to
substitute, we will start over and eliminate x:

---------------------------
       
  9x + 14y =  38
-20x + 21y = 144

Next we eliminate the other variable x:
The coefficients of x are 9 and -20
The least common multiple of 9 and 20
is 180.  To make the coefficients of
x equal in absolute value yet opposite
in sign we multiply the first equation
through by 20 and the second equation
through by 9.  That will make the
coefficients +180 and -180:

20[  9x + 14y] = 20[38]
 9[-20x + 21y] =  9[144]

   180x + 280y =  760
  -180x + 189y = 1296

Now we add those term by term:

   180x + 280y =  760
  -180x + 189y = 1296
  -------------------
          469y = 2056
             y = 

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

So the solution is 

Edwin