Given the equation 4x + 2y = 9, which equation below would cause an inconsistent-independent system?

A:6x + 12y = 13

B: 2x + y = - 6

C:x - 2y = 7

D:8x - 4y = - 5

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.