For what value of k does the point (k, −3) lie on the line 3x − y = 6?

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Solution

Given line: $3 x - y = 6$
Also $(k, - 3)$ lies on the line.
Therefore, putting $x = k, y = - 3$ in the equation of the line, we get:
$3 k - (- 3) = 6 \Rightarrow 3 k + 3 = 6 \Rightarrow 3 k = 3 \Rightarrow k = 1$
Hence, $k = 1$ .

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