Find all of the six-digit numbers in which the first digit is one less than the second,

Let abcdef denote any such six-digit number and convert each requirement in
the problem statement into an equation.
a = b - 1
c =1/2b
d = 3c
10e + f = d + e
24 = a + b + c + d + e + f
In a more standard form this becomes
a - b = -1
-b + 2c = 0
-3c + d = 0
-d + 9e + f = 0
a + b + c + d + e + f = 24
Using equation operations (or the techniques of the upcoming Section RREF), this system can be converted
to the equivalent system

a +16/75f = 5
b + 16/75f = 6
c +8/75f = 3
d + 825f = 9
e +11/75f = 1
Clearly, choosing f = 0 will yield the solution abcde = 563910. Furthermore, to have the variables result in
single-digit numbers, none of the other choices for f (1; 2; ..... ; 9) will yield a solution.