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.
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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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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