The result from the loop is correct.  You are using two different sets of numbers.  Here is the loop computation without loops.

    x = {4/5,31/39}
    y = {2/5, 145/357}
    A = {62243/100000, 3239/6250, 17631/25000}
    A[[3]] - A[[1]]*x - A[[2]]*y