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?