Çözüldü Intercepted Lines - One Variable Linear Equations

Given the five points (4, 0), (-3, 0), (-2, -3), (0, 6), and (0, -2) on the Cartesian plane, if one line passes through three of them and another line passes through the remaining two, what is the sum of the coordinates of their intersection point?

A) -9
B) -10
C) -12
D) -14
E) -15

Note: Slightly changed version of a question from the Turkish 2023 KPSS Exam.

After sketching, which is homework for the interested students, it is observed that:

the line passing two of those points which are (0, 6) and (-3, 0) is,
(y - 6) / (6 - 0) = (x - 0) / [ 0 - (-3) ] ⇒ y = 2x + 6

the line passing three of those points which are (4, 0), (0, -2), (-2, -3), is, by considering only the first two points,
(y - 0) / [ 0 - (-2) ] = (x - 4) / (4 - 0) ⇒ y = x / 2 - 2

The abscissa and ordinate of the interception point are respectively:
2x + 6 = x / 2 - 2 ⇒ x = -16 / 3 ⇒ y = 2(-16 / 3) + 6 = (-32 + 18) / 3 = -14 / 3

The sum of these coordinates is -16 / 3 + (-14 / 3) = -30 / 3 = -10.