Çözüldü Points and Lines - Analytic Geometry

If m is a real number, what is the product of the coordinates of the fixed point where the lines 3m·y + 2x - 4m + 3 = 0 intersect?

A) -3
B) -2
C) 1
D) 2
E) 3

Solution - 1:
Taking any arbitrary values, such as 0 and 1 for m, 2x + 3 = 0 ⇒ x = -3 / 2....(I),
2x + 3y - 1 = 0....(II)
Substituting the value in (I) for its place in (II), 2·(-3 / 2) + 3y - 1 = 0 ⇒ y = 4 / 3....(III)
Multiplying the values in (I) and (III), x·y = (-3 / 2)·(4 / 3) = -2.

Solution - 2:
Arranging the equation of the line for m, (3y - 4)·m + (2x + 3) = 0 ⇒ y = 4 / 3 ∧ x = -3 / 2, then x·y = (-3 / 2)·(4 / 3) = -2.

Source: "ÖSS'ye Hazırlık, Analitik Geometri 1 - 2", Zafer Yayınları, Ekim 2002, Sayfa 30, Çözümlü Örnek