Do the following equations represent a pair of coincident lines? Justify your answer.
$-2x - 3y = 1$
$6y + 4x = -2$

(A) The condition for two lines to be coincident is given by the ratio of their coefficients:
$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
First,rewrite the given equations in the standard form $ax + by + c = 0$:
$1) -2x - 3y - 1 = 0$
$2) 4x + 6y + 2 = 0$
Here,the coefficients are:
$a_1 = -2, b_1 = -3, c_1 = -1$
$a_2 = 4, b_2 = 6, c_2 = 2$
Now,calculate the ratios:
$\frac{a_1}{a_2} = \frac{-2}{4} = -\frac{1}{2}$
$\frac{b_1}{b_2} = \frac{-3}{6} = -\frac{1}{2}$
$\frac{c_1}{c_2} = \frac{-1}{2} = -\frac{1}{2}$
Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} = -\frac{1}{2}$,the given pair of linear equations represents coincident lines.