Question

Find the point of intersection of the lines 4x + 3y = 1 and 3x - y + 9 = 0. If this point lies on the line (2k - 1) x - 2y = 4; find the value of k.

Answer 1

Consider the given equations:
4x + 3y = 1 ….(1)
3x – y + 9 = 0 ….(2)
Multiplying (2) with 3, we have:
9x – 3y = -27 ….(3)
Adding (1) and (3), we get,
13x = -26
x = -2
From (2), y = 3x + 9 = -6 + 9 = 3
Thus, the point of intersection of the given lines (1) and (2) is (-2, 3).
The point (-2, 3) lies on the line (2k – 1)x – 2y = 4.
(2k – 1)(-2) – 2(3) = 4
-4k + 2 – 6 = 4
-4k = 8
k = -2