The system of equations 2x - 3y - 5 = 0 , 15y - 10x + 50 = 0

The given system of equations is:
$2x - 3y - 5 = 0$
$-10x + 15y + 50 = 0$

Comparing with $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$, we have:
$a_1 = 2$, $b_1 = -3$, $c_1 = -5$
$a_2 = -10$, $b_2 = 15$, $c_2 = 50$

Calculating the ratios of the coefficients:
$\dfrac{a_1}{a_2} = \dfrac{2}{-10} = -\dfrac{1}{5}$

$\dfrac{b_1}{b_2} = \dfrac{-3}{15} = -\dfrac{1}{5}$

$\dfrac{c_1}{c_2} = \dfrac{-5}{50} = -\dfrac{1}{10}$

Since $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$, the lines represented by the equations are parallel and distinct.

Thus, the system of equations has no solution and is inconsistent.