Comparing the equations $3x + 2y = 5$ and $2x - 3y = 7$ with standard form, we get $a_1 = 3, b_1 = 2, c_1 = -5$ and $a_2 = 2, b_2 = -3, c_2 = -7$. Calculating the ratios: $\frac{a_1}{a_2} = \frac{3}{2}$ and $\frac{b_1}{b_2} = \frac{2}{-3}$. Since $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$, the lines intersect at a point. Thus, the pair of equations is consistent.

Comparing the equations $2x - 3y = 8$ and $4x - 6y = 9$, we get $a_1 = 2, b_1 = -3, c_1 = -8$ and $a_2 = 4, b_2 = -6, c_2 = -9$. Calculating the ratios: $\frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$, $\frac{b_1}{b_2} = \frac{-3}{-6} = \frac{1}{2}$, and $\frac{c_1}{c_2} = \frac{-8}{-9} = \frac{8}{9}$. Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$, the lines are parallel. Thus, the pair of equations is inconsistent.

Comparing the equations $\frac{3}{2}x + \frac{5}{3}y = 7$ and $9x - 10y = 14$, we get $a_1 = \frac{3}{2}, b_1 = \frac{5}{3}, c_1 = -7$ and $a_2 = 9, b_2 = -10, c_2 = -14$. Calculating the ratios: $\frac{a_1}{a_2} = \frac{3/2}{9} = \frac{1}{6}$ and $\frac{b_1}{b_2} = \frac{5/3}{-10} = -\frac{1}{6}$. Since $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$, the lines intersect. Thus, the pair of equations is consistent.

Comparing the equations $5x - 3y = 11$ and $-10x + 6y = -22$, we get $a_1 = 5, b_1 = -3, c_1 = -11$ and $a_2 = -10, b_2 = 6, c_2 = 22$. Calculating the ratios: $\frac{a_1}{a_2} = \frac{5}{-10} = -\frac{1}{2}$, $\frac{b_1}{b_2} = \frac{-3}{6} = -\frac{1}{2}$, and $\frac{c_1}{c_2} = \frac{-11}{22} = -\frac{1}{2}$. Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, the lines are coincident. Thus, the pair of equations is consistent.

Comparing the equations $\frac{4}{3}x + 2y = 8$ and $2x + 3y = 12$, we get $a_1 = \frac{4}{3}, b_1 = 2, c_1 = -8$ and $a_2 = 2, b_2 = 3, c_2 = -12$. Calculating the ratios: $\frac{a_1}{a_2} = \frac{4/3}{2} = \frac{2}{3}$, $\frac{b_1}{b_2} = \frac{2}{3}$, and $\frac{c_1}{c_2} = \frac{-8}{-12} = \frac{2}{3}$. Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$, the lines are coincident. Thus, the pair of equations is consistent.