On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the following pair of linear equations are consistent or inconsistent.
$3x + 2y = 5; \quad 2x - 3y = 7$

(A) Given equations are:
$3x + 2y - 5 = 0$
$2x - 3y - 7 = 0$
Comparing these with the standard form $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,we get:
$a_{1} = 3, b_{1} = 2, c_{1} = -5$
$a_{2} = 2, b_{2} = -3, c_{2} = -7$
Now,calculating the ratios:
$\frac{a_{1}}{a_{2}} = \frac{3}{2}$
$\frac{b_{1}}{b_{2}} = \frac{2}{-3} = -\frac{2}{3}$
Since $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$,the lines intersect at a single point.
Therefore,the pair of linear equations has a unique solution and is consistent.