Answer
$b_2=2(b_1)$
Work Step by Step
Given,
$ 3x-2y =b_1 \\6x-4y=b_2 $
The equation for the two lines can be rewritten as
$y=(3/2)x-b_1/2\\y=(3/2)x-b_2/4$
We can see that the two lines are parallel since they have equal slopes.
This implies that these lines do not have any point of intersection unless they overlap which will result in infinitely many solutions.
Thus the lines will overlap when the y-intercepts are equal-
$b_1/2=b_2/4$
or
$b_2=2b_1$
The column picture is as follows -
$x\begin{bmatrix}3\\6\end{bmatrix}-y\begin{bmatrix}2\\4\end{bmatrix}=\begin{bmatrix}b_1\\b_2\end{bmatrix}$
