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Reflection of a Point about a Line

The number of...

Question

The number of integer values of $m$ , for which the $x$ -coordinate of the point of intersection of the lines, $3 x + 4 y = 9$ and $y = m x + 1$ is also an integer is

A

- 2

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B

0

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C

4

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D

1

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Solution

The correct option is D $- 2$
Given lines are

$3 x + 4 y = 9$ .........(1)
$y = m x + 1$ ........(2)

$3 x + 4 (m x + 1) = 9$

$3 x + 4 m x = 5$

$x = \frac{5}{3 + 4 m}$

$m = - 2$
for x to be integer.

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