Line up the letters in the equations so that
the letters are in columns, like this

2x + 3y = 5
4x -  y = 3

The idea is to multiply every term in the second 
equation by a number so that if you add the equations
term-by-term one of the letters will cancel.  Let's
eliminate y by multiplying every term in the second 
equation by 3 to make the "- y" become a "3y"

 2x + 3y = 5
12x - 3y = 9

Now draw a line under them like this

 2x + 3y = 5
12x - 3y = 9
------------

Now add corresponding terms and put the result under
the line:

 2x + 3y =  5
12x - 3y =  9
-------------
14x      = 14

When I added the +3y and the -3y, I gor zero, so
I didn't write anything under them, because they
cancelled.

Now we solve 

14x = 14

by dividing both sides by 14 and get

  x = 1.  Now we must get y by sustituting

(1) for y in either of the original two
equations:

  4x - y = 3
4(1) - y = 3
   4 - y = 3

Subtract 4 from both sides

     -y = -1

Write -y as -1y

    -1y = -1

Divide both sides by -1

      y = 1

Edwin