Do the following equations represent a pair of coincident lines? Justify your answer.
$\frac{x}{2} + y + \frac{2}{5} = 0$
$4x + 8y + \frac{5}{16} = 0$

(N/A) The condition for two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to be coincident is $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.
Given equations are:
$1) \frac{1}{2}x + 1y + \frac{2}{5} = 0$
$2) 4x + 8y + \frac{5}{16} = 0$
Here,$a_1 = \frac{1}{2}, b_1 = 1, c_1 = \frac{2}{5}$ and $a_2 = 4, b_2 = 8, c_2 = \frac{5}{16}$.
Calculating the ratios:
$\frac{a_1}{a_2} = \frac{1/2}{4} = \frac{1}{8}$
$\frac{b_1}{b_2} = \frac{1}{8}$
$\frac{c_1}{c_2} = \frac{2/5}{5/16} = \frac{2}{5} \times \frac{16}{5} = \frac{32}{25}$
Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$,the lines are parallel and not coincident. Therefore,the given equations do not represent a pair of coincident lines.