If x = 3k + 2 and y = 2k – 1 is a solution of the equation 4x – 3y + 1 = 0, find the value of k.

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Solution

Given: 4x – 3y + 1 = 0 .....(1)
x = 3k + 2 and y = 2k – 1
Putting these values in the equation (1) we get
$4 (3 k + 2) - 3 (2 k - 1) + 1 = 0 \Rightarrow 12 k + 8 - 6 k + 3 + 1 = 0 \Rightarrow 6 k + 12 = 0 \Rightarrow k + 2 = 0 \Rightarrow k = - 2$

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