guh I didn't exctract it right -.-;
calculating using only 3 elementric functions - multiply an equetion by a constant(=/= 0), adding an equation * constant to another equation, and changing the order of equations.
>.< I though you said something else and then I solved it, and heck it's errorious with a keyboard and the forums font and all >.<
so...
the =0 is not needed because 0 is neutral to subsraction and stays the same with multiplication
(1,0,-1,0) ---> (1,0,-1,0) ----> (1,0,-1,0) ---> (2,0,0,-1)
(2,1,0,-2) ---> (0,1,2,-2) ----> (0,1,2,-2) ---> (0,1,0,-1)
(2,3,-6,-1) ---> (0,3,-4,-1) ----> (0,0,-10,5) ---> (0,0,2,-1)
(0,1,-2,0) ---> (0,1,-2,0) ----> (0,0,-4,2) ---> (0,0,0,0)
and back to eqatuions:
a = 1/2d
b = d
c = 1/2d
that's an infinite number of solutions, like say, (a,b,c,d)=(1,2,1,2)
[ 1 ] Ba(OH)2 + [ 2 ]HNO3 --> [ 1 ] Ba(NO3)2 + [ 2 ] H2O