Two rails are represented by the equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$. Will the rails cross each other?

(B) The given pair of linear equations is:
$x + 2y - 4 = 0$ $...(1)$
$2x + 4y - 12 = 0$ $...(2)$
Comparing these equations with the standard form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:
$a_1 = 1, b_1 = 2, c_1 = -4$
$a_2 = 2, b_2 = 4, c_2 = -12$
Now,we find the ratios of the coefficients:
$\frac{a_1}{a_2} = \frac{1}{2}$
$\frac{b_1}{b_2} = \frac{2}{4} = \frac{1}{2}$
$\frac{c_1}{c_2} = \frac{-4}{-12} = \frac{1}{3}$
Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$,the lines represented by these equations are parallel.
Therefore,the rails will not cross each other.