First slide

Equation of line in Straight lines

Question

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

Moderate

A

2
B

0
C

4
D

1

Solution

The given lines are 3x + 4y = 9 -------(1)
and y = mx + 1 --------(2)
Solving (1) and (2), we get the x-coordinate of the point of intersection as $x = \frac{5}{4 m + 3}$
Since x-coordinate is an integer,
$∴ 4 m + 3 = \pm 5 o r 4 m + 3 = \pm 1$
Solving these, only integer values of m are –1 and –2.
$∴$ m = –1, –2

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