Elementary Number Theory Exercise

x	+y	+z 	= 100  	|(1) this * 10
10x	+10y	+10z	= 1000	| this - (2)
10x	+3y	+0.5z 	= 100 	|(2)
_____________________________
0x	+7y	+9.5z	= 900
	14y	+18z	= 1800

z = (1800 - 14y)/19		|(3)

1800 - 14y = 0 	(mod 19)
14y = 1800 	(mod 19)
y = 1800*15 	(mod 19)
y = 27000 	(mod 19)
y = 1 		(mod 19)

y(k) = 1 + 19k			| substituting in (3) and then in (1)
z(k) = 94 - 14k
x(k) = 5 - 5k

x must be > 0 so k = 0
y(0) = 1, z(0) = 94, x(0) = 5