First slide

Equation of line in Straight lines

Question

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

Moderate

A

2
B

0
C

4
D

1

Solution

The x-coordinate of the point of intersection is 3x + 4 (mx+1) - 9
$or (3 + 4 m) x = 5 or x = \frac{5}{3 + 4 m}$
For x to be an integet,3 + 4m should be a divisor of 5, i.e., of 1, -1, 5, or -5. Hence,
$3 + 4 m = 1 or m = - \frac{1}{2} (not integer)$
$3 + 4 m = - 1 or m = - 1 (integer)$
$3 + 4 m = 5 or m = \frac{1}{2} (not an integer)$
$3 + 4 m = - 5 or m = - 2 (integer)$
Hence, there are two integral values of m.

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