Are the following pair of linear equations consistent? Justify your answer.
$\frac{3}{5} x - y = \frac{1}{2}$
$\frac{1}{5} x - 3 y = \frac{1}{6}$

(A) pair of linear equations is consistent if it has at least one solution. The conditions are:
$1$. $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ (Unique solution)
$2$. $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ (Infinitely many solutions)
Given equations:
$Eq_1: \frac{3}{5} x - y - \frac{1}{2} = 0$
$Eq_2: \frac{1}{5} x - 3 y - \frac{1}{6} = 0$
Comparing with $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$:
$a_1 = \frac{3}{5}, b_1 = -1, c_1 = -\frac{1}{2}$
$a_2 = \frac{1}{5}, b_2 = -3, c_2 = -\frac{1}{6}$
Calculating ratios:
$\frac{a_1}{a_2} = \frac{3/5}{1/5} = 3$
$\frac{b_1}{b_2} = \frac{-1}{-3} = \frac{1}{3}$
Since $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ $(3 \neq \frac{1}{3})$,the system has a unique solution.
Therefore,the given pair of linear equations is consistent.