3a - 12b = 9
14a - 11b = 5

To eliminate a. The LCM of 3 and 14 is 42.
Multiply the first equation thru by 14,
and the second equation by -3

14[ 3a - 12b = 9]
-3[14a - 11b = 5]

   42a - 168b = 126
  -42a +  33b = -15
 -------------------
        -135b = 111
            b = 111/(-135) 
            b = -37/45

Since -37/45 will be hard to substitute into
one of the equations, we start over and
eliminate b:

The LCM of 12 and 11 is 132.
Multiply the first equation thru by 11,
and the second equation by -12

 11[ 3a - 12b = 9]
-12[14a - 11b = 5]

   33a - 132b =  99
 -168a + 132b = -60
 -------------------
 -135a        =  39
            a = 39/(-135) 
            a = -13/45
    
    a = -13/45 b = -37/45

(a, b) = (-13/45, -37/45)        

Edwin
AnlytcPhil@aol.com