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.

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1 Answers

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

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