Consider the equations:
$ x+2y + 2z =1$
and, $ 2x+4y+4z=9$
According to my book, we can infer there are zero solutions from looking at both equations. However, this doesn't make sense to me as, I was taught that we find out about number of solution using the determinant of the coefficients of three equations for a linear system of three variables.
Basically my question is, given two equation of three variables, can we infer about the number of solutions without having a third?
You may simply observe that once multiplied by 2 the first equation becomes $2x+4y+4z=2$. However since $2\neq 9$ we may note that for all values these two equations are inconsistent and so there are no solutions.