x + y + z = 6500
        y = x
        y = z + 500

Solve the second equation for x

        y = x

Multiply both sides by 3 to clear the fraction

       3y = 2x

Divide both sides by 2

       y = x

Now we have something to substitute for x in terms of y
in the first equation. 

Now we need something to substitute for z in terms of y
in the first equation.  So we solve the third equation
for z:

        y = z + 500
  y - 500 = z

Now we substitute y for x, and y - 500 for z
in the first equation:

 x + y + z = 6500

y + y + y - 500 = 6500

Clear the fraction by multiplying through by 2

 3y + 2y + 2y - 1000 = 13000
           7y = 14000
            y = 2000

   y - 500 = z
2000 - 500 = z
      1500 = z

       y = x
  (2000) = x
     3000 = x

The first receives PHP3,000
The second receives PHP2,000
The third receives PHP1,500

Edwin