Determine if the following pairs of linear equations are consistent or inconsistent.

Here, $a_1 = 3$, $b_1 = 2$, $c_1 = -5$
And $a_2 = 2$, $b_2 = -3$, $c_2 = -7$

Since $\frac{3}{2} \neq -\frac{2}{3}$, we have $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.

Therefore, the pair of equations is consistent.

Here, $a_1 = \frac{3}{2}$, $b_1 = \frac{5}{3}$, $c_1 = -7$
And $a_2 = 9$, $b_2 = -10$, $c_2 = -14$

Since $\frac{1}{6} \neq -\frac{1}{6}$, we have $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.

Therefore, the pair of equations is consistent.

Here, $a_1 = -1$, $b_1 = 2$, $c_1 = -8$
And $a_2 = 2$, $b_2 = 3$, $c_2 = -12$

Since $-\frac{1}{2} \neq \frac{2}{3}$, we have $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.

Therefore, the pair of equations is consistent.