Question

If the x-coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is an integer, then the integer value of m is …….

(a) 2

(b) 0

(c) 4

(d) 1

Answer 1

The correct option (a) 2   

Explanation:

lines: 3x + 4y = 9

y = mx + 1

∴ 3x + 4mx + 4 = 9

∴ 3x + 4mx = 5

∴ x = [5/(3 + 4m)]

∴ x co-ordinate of intersection is an integer.

∴ 3 + 4m = ± 1, ± 5.

∴ m = – (1/2), – 2, (1/2), – 1

∴ integer number of m = 2.