SOLUTION: How to solve:3x-y=23,x/3+y/4=4 using the method of elimination by equating coefficients.

3x - y = 23,   (1)
 = 4.      (2)

Multiply equation (2) by 12 (both sides) to rid off the denominators.  You will get


3x -  y = 23,   (1')
4x + 3y = 48.   (2')

To eliminate "y", multiply the equation (1') by 3 (both sides). You will get

9x - 3y = 69,    (1'')
4x + 3y = 48.    (2'')

Now add equations (1'') and (2'')  (both sides).  You will get

9x + 4x = 117  ====>  13x = 117  ====>  x =  = 9.

Now y = 3x - 23 = 3*9 - 23 = 27 - 23 = 4.


Answer.  x = 9,  y = 4.