Been playing with 3x3 equations with coefficients in an arithmetic series..
E.g
x+2y+3z=4
5x+6y+7z=8
9x+10y+11z= 12
Or even this
x+2y+3z=4
9x+11y+13z=15
4x+1y+-2z= -5
( where each separate line is an arithmetic series).
It appears that these types of equations ( been playing with wolfram) appear have no solutions, always??
Can anyone see an easy way why?