Same Problem : Matrix Equation Ax=b

this is what I had for the reduction, I am not sure if it's correct...

column 1 [1 0] column 2 [-1/2 0] column 3 [b1/2 b2/3]

the answer in the back of the book gave the following response:

The equation Ax=b is consistent when 3b1+b2 is nonzero.(I need to show my work to show why it's not consistent). The set of b for which the equation is consistent is a line through the origin- the set of all points (b1,b2) satisfying b2=-3b1.

I don't know what any of this means. Could please explain?

Thank You all for the help!

It is much appreciated!:)