First slide

Equation of line in Straight lines

Question

The number of integer value 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

Moderate

A

2
B

0
C

4
D

1

Solution

x-coordinate of the point of intersection is given by
$3 x + 4 (m x + 1) = 9$
$x = \frac{5}{3 + 4 m}$
As x is an integer, $3 + 4 m_{}$ must be a divisor of 5
SO $3 + 4 m = \pm 1 or \pm 5$
(considering the integer value only)

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