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

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Solution

It is given that $4 x - 3 y + 1 = 0$
Now by substituting the value of $x$ and $y$ in the equation
$4 (3 k + 2) - 3 (2 k - 1) + 1 = 0$
On further calculation
$12 k + 8 - 6 k + 3 + 1 = 0$
$6 k + 12 = 0$
So we get

$6 k = - 12$
By division

$k = - 2$

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