Inconsistent-independent system means that there are no solutions.
Graphically the lines of those equations will never cross - the lines are parallel.
So when the two lines are parallel?
When they have the same A factors.
So when you have an equation 4x+2y=9 we need to rewrite it to
y= -2x+9/2
So the A factor is -2 (it is the number with x) and the B factor is 9/2
So all we need to do now is to find an equation with the same A factor.
Lets rewrite equations in answers:
A: 6x+12y=13 -> y=-1/2x+13/12 A=-1/2 - so it is not an equation we are looking for
B: 2x+y=-6 -> y=-2x-6 A=-2 - this is an equation we were looking for.
C: x-2y=7 -> y=1/2x-7/2 A=1/2 - so it is also not a good answer
The answer is B: the equation 2x+y=-6 will cause the inconsistent-independent system with the given equation.