Let g = cost of gold alloy and s = cost of silver alloy

5g + 20s = 540

4g + 25s = 450

4(5g + 20s) = 4(540)

-5(4g + 25s) = -5(450)

20g + 80s = 2160

-20g - 125s = -2250

          -45s = -90

                      s = 2         5g + 20 (2) = 540 ;  5g +40 = 540;  5g = 500;  g = 100